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Scattering with critically-singular and $δ$-shell potentialsJun 13 2019The authors consider a scattering problem for electric potentials that have a component which is critically singular in the sense of Lebesgue spaces, and a component given by a measure supported on a compact Lipschitz hypersurface. They study direct and ... More

Global well-posedness for low regularity data in the 2d modified Zakharov-Kuznetsov equationJun 13 2019We consider the modified Zakharov-Kuznetsov (mZK) equation in two space dimensions in both focusing and defocusing cases. Using the $I$-method, we prove the global well-posedness of the $H^s$ solutions for $s>\frac{3}{4}$ for any data in the defocusing ... More

Stable self-similar blowup for a family of nonlocal transport equationsJun 13 2019We consider a family of non-local problems that model the effects of transport and vortex stretching in the incompressible Euler equations. Using modulation techniques, we establish stable self-similar blow-up near a family of known self-similar blow-up ... More

Asymptotic stability of equilibria for screened Vlasov-Poisson systems via pointwise dispersive estimatesJun 13 2019We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov-Poisson systems with screened interactions in the whole space $\mathbb{R}^d$ (for $d\geq3$) that was first established by Bedrossian, Masmoudi and Mouhot. Our proof follows ... More

Bounds on the energy of a soft cubic ferromagnet with large magnetostrictionJun 13 2019We complete the analysis initiated in [5] on the micromagnetics of cubic ferromagnets in which the role of magnetostriction is significant. We prove ansatz-free lower bounds for the scaling of the total micromagnetic energy including magnetostriction ... More

Reflection of Willmore surfaces with free boundariesJun 13 2019We study immersed surfaces in $\mathbb{R}^3$ which are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary, and when the boundary is contained ... More

Global branches of solutions for a class of non uniformly fully nonlinear elliptic equationsJun 13 2019We consider singular perturbations of eigenvalue problems. We prove that to these problems correspond simple eigenvalues and we study their asymptotic behavior. As a result, we prove global bifurcation results for non uniformly and fully nonlinear elliptic ... More

Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gasJun 13 2019We are concerned with the one-dimensional piston problem for the compressible Euler equations of Chaplygin gas. If the piston moves at constant subsonic speed to the uniform gas, there exists an integral weak solution for the piston problem, consisting ... More

Discontinuous viscosity solutions of first order Hamilton-Jacobi equationsJun 13 2019We consider the simplest example of a time-dependent first order Hamilton-Jacobi equation, in one space dimension and with a bounded and Lipschitz continuous Hamiltonian which only depends on the spatial derivative. We show that if the initial function ... More

Densities for piecewise deterministic Markov processes with boundaryJun 13 2019We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In our approach ... More

The effect of random dispersal on competitive exclusion -- A reviewJun 13 2019Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical model with two ... More

Stability of the Laughlin phase against long-range interactionsJun 13 2019A natural, ''perturbative'', problem in the modelization of the fractional quantum Hall effect is to minimize a classical energy functional within a variational set based on Laughlin's wave-function. We prove that, for small enough pair interactions, ... More

A Noninequality for the Fractional GradientJun 13 2019In this paper we give a streamlined proof of an inequality recently obtained by the author: For every $\alpha \in (0,1)$ there exists a constant $C=C(\alpha,d)>0$ such that \begin{align*} \|u\|_{L^{d/(d-\alpha),1}(\mathbb{R}^d;\mathbb{R}^d)} \leq C \| ... More

Observations on a theorem of Almgren and LiebJun 13 2019In 1989 Almgren and Lieb proved a rearrangement inequality for the Sobolev spaces of fractional order $W^{s,p}$. When $p=2$ the square of the seminorm in $W^{s,2}$ of an indicator function is the nonlocal perimeter of Caffarelli, Roquejoffre and Savin. ... More

Weak type $(1,1)$ bounds for Schrödinger groupsJun 13 2019Let $L$ be a non-negative self-adjoint operator acting on $L^2(X)$ where $X$ is a space of homogeneous type with a dimension $n$. Suppose that the heat kernel of $L$ satisfies a Gaussian upper bound. It is known that the operator $(I+L)^{-s } e^{itL}$ ... More

Structure of singularities in the nonlinear nerve conduction problemJun 12 2019We give a characterisation of the singular points of the free boundary $\partial \{u>0\}$ for viscosity solutions of the nonlinear equation \begin{equation}F(D^2 u)=-\chi_{\{u>0\}},\tag{0.1} \end{equation} where $F$ is a fully nonlinear elliptic operator ... More

Homogenization results for a coupled system of reaction-diffusion equationsJun 12 2019The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying several metabolic ... More

Identifying and Predicting Parkinson's Disease Subtypes through Trajectory Clustering via Bipartite NetworksJun 12 2019Parkinson's disease (PD) is a common neurodegenerative disease with a high degree of heterogeneity in its clinical features, rate of progression, and change of variables over time. In this work, we present a novel data-driven, network-based Trajectory ... More

Analyticity of Steklov eigenvalues of nearly-circular and nearly-spherical domainsJun 12 2019We consider the Dirichlet-to-Neumann operator (DNO) on nearly-circular and nearly-spherical domains in two and three dimensions, respectively. Treating such domains as perturbations of the ball, we prove the analyticity of the DNO with respect to the ... More

A sufficient condition for uniqueness of weak solutions of the incompressible Euler systemJun 12 2019We give a new sufficient criteria to prove the uniqueness of the incompressible Euler equation in dimension $N\geq2$. In their celebrated works by V. Scheffer [18], A. Shnirelman [19], C. De Lellis and L. Sz\'ekelyhidi Jr. [7] they have obtained the nonuniqeness ... More

Global optimization using Sobol indicesJun 12 2019We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method should be ... More

A Liouville-type theorem in a half-space and its applications to the gradient blow-up behavior for superquadratic diffusive Hamilton-Jacobi equationsJun 12 2019We consider the elliptic and parabolic superquadratic diffusive Hamilton-Jacobi equations with homogeneous Dirichlet conditions. For the elliptic problem in a half-space, we prove a Liouville-type classification, or symmetry result, which asserts that ... More

Long time behavior of the solutions of NLW on the d-dimensional torusJun 12 2019We consider the non linear wave equation (NLW) on the d-dimensional torus with an smooth nonlinearity of order at least two at the origin. We prove that, for almost all mass, small smooth solutions of high Sobolev indices are stable up to arbitrary long ... More

Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibriumJun 12 2019This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a background magnetic ... More

Desingularization of matrix equations employing hypersingular integrals in boundary element methods using double nodesJun 12 2019In boundary element methods, the method of using double nodes at corners is a useful approach to uniquely define the normal direction of boundary elements. However, matrix equations constructed by conventional boundary integral equations (CBIE) become ... More

Singular solutions of elliptic equations with iterated exponentialsJun 12 2019We construct positive singular solutions for the problem $-\Delta u=\lambda \exp (e^u)$ in $B_1\subset \mathbb{R}^n$ ($n\geq 3$), $u=0$ on $\partial B_1$, having a prescribed behaviour around the origin. Our study extends the one in Y. Miyamoto [Y. Miyamoto, ... More

Continuity results for degenerate diffusion equations with $L^{p}_t L^{q}_{x}$ driftsJun 12 2019In this paper, we study local uniform continuity of nonnegative weak solutions to degenerate diffusion-drift equations in the form \[ u_{t} = \Delta u^{m} + \nabla\cdot \left( B (x,t) \, u\right), \quad \text{for } m \geq 1 \] assuming a vector field ... More

Remarks on large time behavior of level-set mean curvature flow equations with driving and source termsJun 12 2019We study a level-set mean curvature flow equation with driving and source terms, and establish convergence results on the asymptotic behavior of solutions as time goes to infinity under some additional assumptions. We also study the associated stationary ... More

Displacements representations for the problems with spherical and circular material surfaces with surface tensionJun 11 2019The displacements representations of the type used by Christensen and Lo (1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations ... More

Positivity of the fundamental solution for fractional diffusion and wave equationsJun 11 2019We study the question of positivity of the fundamental solution for fractional diffusion and wave equations of the form, which may be of fractional order both in space and time. We give a complete characterization for the positivity of the fundamental ... More

The radiation field on product conesJun 11 2019We consider the wave equation on a product cone and find a joint asymptotic expansion for forward solutions near null and future infinities. The rates of decay seen in the expansion are the resonances of a hyperbolic cone on the "northern cap" of the ... More

Improved regularity for the porous medium equation along zero level-setsJun 11 2019In the present work we establish sharp regularity estimates for the solutions of the porous medium equation, along their zero level-sets. We work under a proximity regime on the exponent governing the nonlinearity of the problem. Then, we prove that solutions ... More

Asymptotic analysis of exit time for dynamical systems with a single well potentialJun 11 2019We study the exit time from a bounded multi-dimensional domain $\Omega$ of the stochastic process $\mathbf{Y}_\varepsilon=\mathbf{Y}_\varepsilon(t,a)$, $t\geqslant 0$, $a\in \mathcal{A}$, governed by the overdamped Langevin dynamics \begin{equation*} ... More

New Examples on Lavrentiev Gap Using FractalsJun 11 2019Jun 13 2019Zhikov showed 1986 with his famous checkerboard example that functionals with variable exponents can have a Lavrentiev gap. For this example it was crucial that the exponent had a saddle point whose value was exactly the dimension. In 1997 he extended ... More

New Examples on Lavrentiev Gap Using FractalsJun 11 2019Zhikov showed 1986 with his famous checkerboard example that functionals with variable exponents can have a Lavrentiev gap. For this example it was crucial that the exponent had a saddle point whose value was exactly the dimension. In 1997 he extended ... More

Existence Theory for the EED Inpainting ProblemJun 11 2019We establish an existence theory for an elliptic boundary value problem in image analysis known as edge-enhancing diffusion (EED) inpainting. The EED inpainting problem aims at restoring missing data in an image as steady state of a nonlinear anisotropic ... More

A proof of the mean-field limit for $λ$-convex potentials by $Γ$-ConvergenceJun 11 2019In this work we give a proof of the mean-field limit for $\lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows of functionals ... More

The incompressible limit of compressible finitely extensible nonlinear bead-spring chain models for dilute polymeric fluidsJun 11 2019We explore the behaviour of global-in-time weak solutions to a class of bead-spring chain models, with finitely extensible nonlinear elastic (FENE) spring potentials, for dilute polymeric fluids. In the models under consideration the solvent is assumed ... More

Study of semi-linear $σ$-evolution equations with frictional and visco-elastic dampingJun 11 2019In this article, we study semi-linear $\sigma$-evolution equations with double damping including frictional and visco-elastic damping for any $\sigma\ge 1$. We are interested in investigating not only higher order asymptotic expansions of solutions but ... More

Direct Characterization of Spectral Stability of Small Amplitude Periodic Waves in Scalar Hamiltonian Problems Via Dispersion RelationJun 11 2019Various approaches to studying the stability of solutions of nonlinear PDEs lead to explicit formulae determining the stability or instability of the wave for a wide range of classes of equations. However, these are typically specialized to a particular ... More

The $C^0$ estimate for the quaternionic Calabi conjectureJun 11 2019We prove the $C^0$ estimate for the quaternionic Monge-Amp\`ere equation on compact hyperK\"ahler with torsion manifolds. Our goal is to provide a simpler proof than the one presented by Alesker and Shelukhin.

Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problemsJun 11 2019In this paper we construct the smallest semigroup $\mathscr{S}$ that dominates a given family of linear Feller semigroups. The semigroup $\mathscr{S}$ will be referred to as the semigroup envelope or Nisio semigroup. In a second step we investigate strong ... More

Normal forms and invariant manifolds for nonlinear, non-autonomous PDEs, viewed as ODEs in infinite dimensionsJun 11 2019We prove that a general class of nonlinear, non-autonomous ODEs in Fr\'echet spaces are close to ODEs in a specific normal form, where closeness means that solutions of the normal form ODE satisfy the original ODE up to a residual that vanishes up to ... More

Uniqueness of determining the variable fractional order in variable-order time-fractional diffusion equationsJun 11 2019We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be determined by ... More

Anderson-Bernoulli Localization on the 3D lattice and discrete unique continuation principleJun 11 2019We consider the Anderson model with Bernoulli potential on $\mathbb{Z}^{3}$, and prove localization of eigenfunctions corresponding to eigenvalues near zero, the lower boundary of the spectrum. The proof follows the framework by Bourgain--Kenig and Ding--Smart. ... More

A method for identifying stability regimes using roots of a reduced-order polynomialJun 10 2019For dispersive Hamiltonian partial differential equations of order 2N+1, N integer, there are two criteria to analyse to examine the stability of small-amplitude, periodic travelling wave solutions to high-frequency perturbations. The first necessary ... More

A physically-consistent, flexible and efficient strategy to convert local boundary conditions into nonlocal volume constraintsJun 10 2019Nonlocal models provide exceptional simulation fidelity for a broad spectrum of scientific and engineering applications. However, wider deployment of nonlocal models is hindered by several modeling and numerical challenges. Among those, we focus on the ... More

First-order linear evolution equations with càdlàg-in-time solutionsJun 10 2019In this work we study first-order linear parabolic evolution PDEs over $\mathbb{R}^{d}\times\mathbb{R}$ and $\mathbb{R}^{d}\times\mathbb{R}^{+}$ comprising a spatial operator defined through a symbol function and a source term such that its spatial Fourier ... More

Models of dynamic damage and phase-field fracture, and their various time discretisationsJun 10 2019Several variants of models of damage in viscoelastic continua under small strains in the Kelvin-Voigt rheology are presented and analyzed by using the Galerkin method. The particular case, known as a phase-field fracture approximation of cracks, is discussed ... More

On Mean Field Limit and Quantitative Estimates with a Large Class of Singular Kernels: Application to the Patlak-Keller-Segel ModelJun 10 2019In this note, we propose a new relative entropy combination of the methods developed by P.--E. Jabin and Z.~Wang [Inventiones (2018)] and by S. Serfaty [Proc. Int. Cong. of Math, (2018) and references therein] to treat more general kernels in mean field ... More

Hyperbolic boundary problems with large oscillatory coefficients: multiple amplificationJun 10 2019We study weakly stable hyperbolic boundary problems with highly oscillatory coefficients that are large, $O(1)$, compared to the small wavelength $\eps$ of oscillations. Such problems arise, for example, in the study of classical questions concerning ... More

A general thermodynamical model for adhesive frictional contacts between viscoelastic or poro-viscoelastic bodies at small strainsJun 10 2019A general model covering a large variety of the so-called adhesive or cohesive, possibly also frictional, contact interfaces between visco-elastic bodies with inertia considered in a thermodynamical context is presented. A semi-implicit time discretisation ... More

A higher speed type II blowup for the five dimensional energy critical heat equationJun 10 2019This paper is concerned with blow-up solutions of the five dimensional energy critical heat equation $u_t=\Delta u+|u|^\frac{4}{3}u$. A goal of this paper is to show the existence of type II blowup solutions which behave as $\|u(t)\|_\infty\sim(T-t)^{-3k}$ ... More

Global existence of weak solutions to the compressible quantum Navier-Stokes equations with degenerate viscosityJun 10 2019We study the compressible quantum Navier-Stokes (QNS) equations with degenerate viscosity in the three dimensional periodic domains. On the one hand, we consider QNS with additional damping terms. Motivated by the recent works [Li-Xin, arXiv:1504.06826] ... More

Morse theory for the Yang-Mills energy function near flat connectionsJun 10 2019A result (Corollary 4.3) in an article by Uhlenbeck (1985) asserts that the $W^{1,p}$-distance between the gauge-equivalence class of a connection $A$ and the moduli subspace of flat connections $M(P)$ on a principal $G$-bundle $P$ over a closed Riemannian ... More

Global smooth solutions of the 3D Hall-magnetohydrodynamic equations with large dataJun 10 2019In this paper, we establish the global existence to the three-dimensional incompressible Hall-MHD equations for a class of large initial data, whose $L^{\infty}$ norms can be arbitrarily large. In addition , we give an example to show that such a large ... More

Global smooth solutions of the generalized MHD equations with large dataJun 10 2019In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term. Precisely speaking, ... More

A Lyapunov Approach to Robust Regulation of Distributed Port-Hamiltonian SystemsJun 10 2019This paper studies robust output tracking and disturbance rejection for boundary controlled infinite-dimensional port-Hamiltonian systems including second order models such as the Euler-Bernoulli beam. The control design is achieved using the internal ... More

Long-time behavior for three dimensional compressible viscous and heat-conductive gasesJun 10 2019We study the large-time behavior of solutions to the compressible Navier-Stokes equations for a viscous and heat-conductive gases in $\mathbb{R}^3$. More precisely, under a suitable additional condition involving only the low frequencies of the initial ... More

Elliptic variational problems with mixed nonlinearitiesJun 10 2019In this paper, we study the existence and multiplicity results of nontrivial positive solutions to a quasilinear elliptic equation in $\RN$, when $N\geq2$, as \begin{equation} \Lp u+u^{p-1}=\lambda\hspace{0.2mm}k(x)u^{r-1}-h(x)u^{q-1}.\nonumber \end{equation} ... More

Proposal to Use the Fractional Derivative of Radial Functions in Interpolation ProblemsJun 10 2019In this document we present the construction of a radial functions that have the objective of emulating the behavior of the radial basis function thin plate spline (TPS), which we will name as function TPS, we propose a way to partially and totally apply ... More

Nonlinear elliptic equations on the upper half spaceJun 10 2019In this paper we shall classify all positive solutions of $ \Delta u =a u^p$ on the upper half space $ H =\Bbb{R}_+^n$ with nonlinear boundary condition $ {\partial u}/{\partial t}= - b u^q $ on $\partial H$ for both positive parameters $a, \ b>0$. We ... More

On pointwise convergence of Schrödinger meansJun 09 2019For functions in the Sobolev space $H^s$ and decreasing sequences $t_n\to 0$ we examine convergence almost everywhere of the generalized Schr\"odinger means on the real line, given by \[S^af(x,t_n)=\exp( it_n (-\partial_{xx})^{a/2})f(x);\] here $a>0$, ... More

Segregation and Gap Formation in Cross-Diffusion ModelsJun 09 2019In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the population pressure ... More

Bounded $H_{\infty}$-calculus for Boundary Value Problems on Manifolds with Conical SingularitiesJun 09 2019Realizations of differential operators subject to differential boundary conditions on manifolds with conical singularities are shown to have a bounded $H_\infty$-calculus in appropriate $L_p$-Sobolev spaces provided suitable conditions of parameter-ellipticity ... More

Geometric Partial Differential Equations from Unified String TheoriesJun 09 2019An informal introduction to some new geometric partial differential equations motivated by string theories is provided. Some of these equations are also interesting from the point of view of non-K\"ahler geometry and the theory of non-linear partial differential ... More

Non-boundedness of the number of nodal domains of a sum of eigenfunctionsJun 09 2019Generalizing Courant's nodal domain theorem, the ``Extended Courant property'' is the statement that a linear combination of the first $n$ eigenfunctions has at most $n$ nodal domains. In the first part of the paper, we prove that the Extended Courant ... More

Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood--Paley Characterizations and Real InterpolationJun 09 2019Let $X$ be a ball quasi-Banach function space on ${\mathbb R}^n$. In this article, assuming that the powered Hardy--Littlewood maximal operator satisfies some Fefferman--Stein vector-valued maximal inequality on $X$ as well as it is bounded on both the ... More

A Lorentz-Covariant Interacting Electron-Photon System in One Space DimensionJun 09 2019A Lorenz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac's formalism of multi-time wave functions, ... More

Efficient invariant energy quadratization and scalar auxiliary variable approaches without bounded below restriction for phase field modelsJun 09 2019Recently introduced invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches have proven to be very powerful ways to construct energy stable schemes for phase field models. Both methods require the square root functions are ... More

On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical RegimeJun 09 2019By using the pseudo-metric introduced in [F. Golse, T. Paul: Archive for Rational Mech. Anal. 223 (2017) 57-94], which is an analogue of the Wasserstein distance of exponent $2$ between a quantum density operator and a classical (phase-space) density, ... More

Neurogeometry of perception: isotropic and anisotropic aspectsJun 08 2019In this paper we first recall the definition of geometical model of the visual cortex, focusing in particular on the geometrical properties of horizontal cortical connectivity. Then we recognize that histograms of edges - co-occurrences are not isotropic ... More

On statistical Calderón problemsJun 08 2019For $D$ a bounded domain in $\mathbb R^d, d \ge 3,$ with smooth boundary $\partial D$, the non-linear inverse problem of recovering the unknown conductivity $\gamma$ determining solutions $u=u_{\gamma, f}$ of the partial differential equation \begin{equation*} ... More

Optimal control of time and therapy in a tumor growth model with possibly singular potentialsJun 08 2019A distributed optimal control problem for a diffuse interface model which physical context is that of tumor growth dynamics is discussed. The system we deal with consists of a Cahn-Hilliard equation for the tumor phase coupled with a reaction-diffusion ... More

Uniqueness and Regularity of Unbounded Weak Solutions to a Class of Cross Diffusion SystemsJun 08 2019We establish the uniqueness and regularity of weak (and very weak) solutions to a class of cross diffusion systems which is inspired by models in mathematical biology/ecology, in particular the Shigesada-Kawasaki-Teramoto (SKT) model in population biology. ... More

Decay of solitary wavesJun 08 2019In this paper we consider the decay rate of solitary-wave solutions to some classes of non-linear and non-local dispersive equations, including for example the Whitham equation and a Whitham--Boussinesq system. The dispersive term is represented by a ... More

Local and global well-posedness for a quadratic Schrödinger system on spheres and Zoll manifoldsJun 07 2019We consider the initial value problem (IVP) associated to a quadratic Schr\"odinger system \begin{equation*} \begin{cases} i \partial_{t} v \pm \Delta_{g} v - v = \epsilon_{1} u \bar{v}, & t \in \mathbb{R},\; x \in M, \\[2ex] i \sigma \partial_{t} u \pm ... More

Well-Posed Final Value Problems and Duhamel's Formula for Coercive Lax--Milgram OperatorsJun 07 2019This paper treats parabolic final value problems generated by coercive Lax--Milgram operators, and well-posedness is proved for this large class. The result is obtained by means of an isomorphism between Hilbert spaces containing the data and solutions. ... More

Global a priori bounds for weak solutions of quasilinear elliptic systems with nonlinear boundary conditionJun 07 2019In this paper we study quasilinear elliptic systems with nonlinear boundary condition with fully coupled perturbations even on the boundary. Under very general assumptions our main result says that each weak solution of such systems belongs to $L^\infty(\close)\times ... More

Blowup on an arbitrary compact set for a Schödinger equation with nonlinear source termJun 07 2019We consider the nonlinear Schr\"odinger equation on ${\mathbb R}^N $, $N\ge 1$, \begin{equation*} \partial _t u = i \Delta u + \lambda | u |^\alpha u \quad \mbox{on ${\mathbb R}^N $, $\alpha>0$,} \end{equation*} with $\lambda \in {\mathbb C}$ and $\Re ... More

The Boltzmann equation with an external force on the torus: Incompressible Navier-Stokes-Fourier hydrodynamical limitJun 07 2019We study the Boltzmann equation with external forces, not necessarily deriving from a potential, in the incompressible Navier-Stokes perturbative regime. On the torus, we establish local-in-time, for any time, Cauchy theories that are independent of the ... More

Navier-Stokes equations with external forces in Besov-Morrey spacesJun 07 2019We establish the existence and uniqueness of local strong solutions to the Navier-Stokes equations with arbitrary initial data and external forces in the homogeneous Besov-Morrey space. The local solutions can be extended globally in time provided the ... More

Partial Regularity in Time for the Space Homogeneous Landau Equation with Coulomb PotentialJun 06 2019We prove that the set of singular times for weak solutions of the space homogeneous Landau equation with Coulomb potential constructed as in [C. Villani, Arch. Rational Mech. Anal. 143 (1998), 273-307] has Hausdorff dimension at most 1/2.

Orlicz Sobolev Inequalities and the Doubling ConditionJun 06 2019In [12] it has been shown that $(p,q)$ Sobolev inequality with $p>q$ implies the doubling condition on the underlying measure. We show that even weaker Orlicz-Sobolev inequalities, where the gain on the left-hand side is smaller than any power bump, imply ... More

Fractional elliptic problems with nonlinear gradient sources and measuresJun 06 2019In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient non-linearity ... More

Monge-Ampère equation with bounded periodic dataJun 06 2019We consider the Monge-Amp\`ere equation $\det(D^2u)=f$ in $\mathbb{R}^n$, where $f$ is a positive bounded periodic function. We prove that $u$ must be the sum of a quadratic polynomial and a periodic function. For $f\equiv 1$, this is the classic result ... More

The Navier--Stokes equations in exterior Lipschitz domains: $\mathrm{L}^p$-theoryJun 06 2019We show that the Stokes operator defined on $\mathrm{L}^p_{\sigma} (\Omega)$ for an exterior Lipschitz domain $\Omega \subset \mathbb{R}^n$ $(n \geq 3)$ admits maximal regularity provided that $p$ satisfies $| 1/p - 1/2| < 1/(2n) + \varepsilon$ for some ... More

The $p$-Adic Scattering equationJun 06 2019There are several techniques in classical case for some PDEs, involving the concept of entropy to show convergence of solutions to a steady state. In this work we deal with the $p$-adic scattering equation and we try to adapt these methods to prove convergence ... More

Double phase transonic flow problems with variable growth: nonlinear patterns and stationary wavesJun 06 2019In this paper we are concerned with a class of double phase energy functionals arising in the theory of transonic flows. Their main feature is that the associated Euler equation is driven by the Baouendi-Grushin operator with variable coefficient. This ... More

An Inverse Optimization Approach to Measuring Clinical Pathway ConcordanceJun 06 2019Clinical pathways outline standardized processes in the delivery of care for a specific disease. Patient journeys through the healthcare system, though, can deviate substantially from recommended or reference pathways. Given the positive benefits of clinical ... More

Crack growth by vanishing viscosity in planar elasticityJun 06 2019We show the existence of quasistatic evolutions in a fracture model for brittle materials by a vanishing viscosity approach, in the setting of planar linearized elasticity. The crack is not prescribed a priori and is selected in a class of (unions of) ... More

Global stability for nonlinear wave equations with multi-localized initial dataJun 06 2019In this paper, we initiate the study of the global stability of nonlinear wave equations with initial data that are not required to be localized around a single point. More precisely, we allow small initial data localized around any finite collection ... More

Self-intersecting interfaces for stationary solutions of the two-fluid Euler equationsJun 06 2019We prove that there are stationary solutions to the 2D incompressible free boundary Euler equations with two fluids, possibly with a small gravity constant, that feature a splash singularity. More precisely, in the solutions we construct the interface ... More

Well-posedness and exponential decay estimates for a Korteweg-de Vries-Burgers equation with time-delayJun 06 2019We consider the KdV-Burgers equation and its linear version in presence of a delay feedback. We prove well-posedness of the models and exponential decay estimates under appropriate conditions on the damping coefficients. Our arguments rely on a Lyapunov ... More

Quantum strips in higher dimensionsJun 06 2019We consider the Dirichlet Laplacian in unbounded strips on ruled surfaces in any space dimension. We locate the essential spectrum under the condition that the strip is asymptotically flat. If the Gauss curvature of the strip equals zero, we establish ... More

Symmetry of Positive Solutions for the Fractional Schr$ \ddot{\textrm{o}}$dinger Equations with Choquard-type NonlinearitiesJun 06 2019This paper deals with the following fractional Schr$ \ddot{\textrm{o}}$dinger equations with Choquard-type nonlinearities \begin{equation*} \left\{\begin{array}{r@{\ \ }c@{\ \ }ll} (-\Delta)^{\frac{\alpha}{2}}u + u - C_{n,-\beta} \,(|x|^{\beta-n}\ast ... More

Negatively Curved Three-Manifolds, Hyperbolic Metrics, Isometric Embedding In Minkowski Space And The Cross Curvature FlowJun 06 2019This short note is a mostly expository article examining negatively curved three-manifolds. We look at some rigidity properties related to isometric embeddings into Minkowski space. We also review the Cross Curvature Flow (XCF) as a tool to study the ... More

On well-posedness of generalized Hall-magneto-hydrodynamicsJun 05 2019We obtain local well-posedness result for the generalized Hall-magneto-hydrodynamics system in Besov spaces ${\dot B^{-(2\alpha_1-\gamma)}_{\infty, \infty}} \times {\dot B^{-(2\alpha_2-\beta)}_{\infty, \infty}(\mathbb R^3)}$ with suitable indexes $\alpha_1, ... More

Quasi-invariance of fractional Gaussian fields nonlinear wave equation with polynomial nonlinearityJun 05 2019We prove quasi-invariance of Gaussian measures $\mu_s$ with Cameron-Martin space $H^s$ under the flow of the defocusing nonlinear wave equation with polynomial nonlinearities of any order for all $s>5/2$, including fractional $s$. This extends work of ... More

Ill-posedness of the Thirring model below the critical regularityJun 05 2019We consider a nonlinear $L^2$-critical nonlinear Dirac equation in one space dimension known as the Thirring model. Global well-posedness in $L^2$ for this equation was proved by Candy. Here we prove that the equation is ill posed in $L^p$ for $1 \le ... More