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Higher Regularity of Weak Limits of Willmore Immersions IIApr 22 2019We obtain in arbitrary codimension a removability result on the order of singularity of Willmore surfaces realising the width of Willmore min-max problems on spheres. As a consequence, out of the twelve families of non-planar minimal surfaces in $\mathbb{R}^3$ ... More

Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentialsApr 21 2019We obtain quasimode, eigenfunction and spectral projection bounds for Schr\"odinger operators, $H_V=-\Delta_g+V(x)$, on compact Riemannian manifolds $(M,g)$ of dimension $n\ge2$, which extend the results of the third author~\cite{sogge88} corresponding ... More

Global classical solutions to an evolutionary model for magnetoelasticityApr 21 2019In this paper, we first prove the local-in-time existence of the evolutionary model for magnetoelasticity with finite initial energy by employing the nonlinear iterative approach given in \cite{Jiang-Luo-2019-SIAM} to deal with the geometric constraint ... More

Criteria for the a-contraction and stability for the piecewise-smooth solutions to hyperbolic balance lawsApr 20 2019We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas in particular. ... More

Stability and uniqueness for piecewise smooth solutions to Burgers-Hilbert among a large class of solutionsApr 20 2019In this paper, we show uniqueness and stability for the piecewise-smooth solutions to the Burgers--Hilbert equation constructed in Bressan and Zhang [Commun. Math. Sci., 15(1):165--184, 2017]. The Burgers--Hilbert equation is $u_t+(\frac{u^2}{2})_x=\mathbf{H}[u]$ ... More

Estimating Sparse Networks with HubsApr 20 2019Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks in such applications ... More

Online Non-stationary Time Series Analysis and ProcessingApr 19 2019Time series analysis is critical in academic communities ranging from economics, transportation science and meteorology, to engineering, genetics and environmental sciences. In this paper, we will firstly model a time series as a non-stationary stochastic ... More

Regularity for the fully nonlinear parabolic thin obstacle problemApr 19 2019We prove $C^{1, \alpha}$ regularity (in the parabolic sense) for the viscosity solution of a boundary obstacle problem with a fully nonlinear parabolic equation in the interior. Following the method which was first introduced for the harmonic case by ... More

High temperature convergence of the KMS boundary conditions: The Bose-Hubbard model on a finite graphApr 19 2019The Kubo-Martin-Schwinger condition is a widely studied fundamental property in quantum statistical mechanics which characterises the thermal equilibrium states of quantum systems. In the seventies, G. Gallavotti and E. Verboven, proposed an analogue ... More

Estimates and monotonicity for a heat flow of isometric G2-structuresApr 18 2019Given a $7$-dimensional compact Riemannian manifold $\left( M,g\right) $ that admits $G_{2}$-structure, all the $G_{2}$-structures that are compatible with the metric $g$ are parametrized by unit sections of an octonion bundle over $M$. We define a natural ... More

The stochastic thin-film equation: existence of nonnegative martingale solutionsApr 18 2019We consider the stochastic thin-film equation with colored Gaussian Stratonovich noise and establish the existence of nonnegative weak (martingale) solutions. The construction is based on a Trotter-Kato-type decomposition into a deterministic and a stochastic ... More

Geometric regularity for elliptic equations in double-divergence formApr 18 2019In this paper, we examine the regularity of the solutions to the double-divergence equation. We establish improved H\"older continuity as solutions approach their zero level-sets. In fact, we prove that $\alpha$-H\"older continuous coefficients lead to ... More

Exact constructions in the (non-linear) planar theory of elasticity: From elastic crystals to nematic elastomersApr 18 2019In this article we deduce necessary and sufficient conditions for the presence of `Conti-type', highly symmetric, exactly-stress free constructions in the geometrically non-linear, planar $n$-well problem, generalising results of [CKZ17]. Passing to the ... More

Phase transition in the exclusion process on the Sierpinski gasket with slowed boundary reservoirsApr 18 2019We derive the macroscopic laws that govern the evolution of the density of particles in the exclusion process evolving on the Sierpinski gasket in the presence of a slow boundary. Depending on the slowness of the boundary we obtain, at the hydrodynamics ... More

Rellich, Gagliardo-Nirenberg and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applicationsApr 18 2019In this paper we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Caffarelli-Kohn-Nirenberg inequalities and the uncertainty principle for Dunkl operators. Moreover, we introduce an extension of the classical Caffarelli-Kohn-Nirenberg ... More

The Euler equations in a critical case of the generalized Campanato spaceApr 18 2019In this paper we prove local in time well-posedness for the incompressible Euler equations in $\Bbb R^n$ for the initial data in $\mathscr {L}^{ 1}_{ 1(1)}(\mathbb {R}^{n}) $, which corresponds to a critical case of the generalized Campanato spaces $ ... More

On equivalence of third order linear differential operators on two-dimensional manifoldsApr 18 2019We study differential invariants of the third order linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles on two dimensional manifolds with respect to groups of authomorphisms.

Slightly Compressible Forchheimer Flows in Rotating Porous Media. IApr 18 2019We formulate the the generalized Forchheimer equations for the three-dimensional fluid flows in rotating porous media. By implicitly solving the momentum in terms of the pressure's gradient, we derive a degenerate parabolic equation for the density in ... More

The subelliptic heat kernel of the octonionic Hopf fibrationApr 18 2019We study the sub-Laplacian of the 15-dimensional unit sphere which is obtained by lifting with respect to the Hopf fibration the Laplacian of the octonionic projective space. We obtain explicit formulas for its heat kernel and deduce an expression for ... More

The Navier-Stokes - End-Functionalized Polymer System: Global Regularity and Polymer Drag ReductionApr 17 2019Reducing wall drag in turbulent pipe and channel flows is an issue of great practical importance. In engineering applications, end-functionalized polymer chains are often employed as agents to reduce drag. These are polymers which are floating in the ... More

Bounds on eigenvalues of perturbed Lamé operators with complex potentialsApr 17 2019Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. This paper provides ... More

Ancient and Eternal Solutions to Mean Curvature Flow from Minimal SurfacesApr 17 2019We construct embedded ancient solutions to mean curvature flow related to certain classes of unstable minimal hypersurfaces in $\mathbb{R}^{n+1}$ for $2 \leq n \leq 6$. These ancient solutions are not solitons, meaning that they do not evolve by rigid ... More

Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flowApr 17 2019We prove a uniform diameter bound for long time solutions of the normalized Kahler-Ricci flow on an $n$-dimensional projective manifold $X$ with semi-ample canonical bundle under the assumption that the Ricci curvature is uniformly bounded for all time ... More

Decays for Kelvin-Voigt damped wave equations I : the black box perturbative methodApr 17 2019We show in this article how perturbative approaches~from our work with Hitrik (see also the work by Anantharaman-Macia) and the {\em black box} strategy from~ our work with Zworski allow to obtain decay rates for Kelvin-Voigt damped wave equations from ... More

Solutions for fractional operator problem via local Pohozaev identitiesApr 17 2019We consider the following fractional Schr\"{o}dinger equation involving critical exponent: \begin{equation*} \left\{\begin{array}{ll} (-\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \ \hbox{ in } \ \mathbb{R}^N, \\ u>0, \ y \in \mathbb{R}^N, \end{array}\right. ... More

A Convection-Diffusion model on a star shaped treeApr 17 2019In this paper we consider a convection-diffusion equation on a star-shaped tree formed by $n$ incoming edges and $m$ outgoing edges. The nonlinearity we consider is of the form $f(u)=|u|^{q-1}u$, $q>1$. We prove the global well-posedness of the solutions ... More

Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flowsApr 17 2019In this paper, we study the three-dimensional non-isentropic compressible fluid-particle flows. The system involves coupling between the Vlasov-Fokker-Planck equation and the non-isentropic compressible Navier-Stokes equations through momentum and energy ... More

The oriented mailing problem and its convex relaxationApr 17 2019In this note we introduce a new model for the mailing problem in branched transportation in order to allow the cost functional to take into account the orientation of the moving particles. This gives an effective answer to [Problem 15.9] of the book "Optimal ... More

Nonparametric drift estimation for diffusions with jumps driven by a Hawkes processApr 17 2019We consider a 1-dimensional diffusion process X with jumps. The particularity of this model relies in the jumps which are driven by a multidimensional Hawkes process denoted N. This article is dedicated to the study of a nonparametric estimator of the ... More

Transport equation in generalized Campanato spacesApr 17 2019In this paper we study the transport equation in $\mathbb{R}^n \times (0,T)$, $T >0$, \[ \partial _t f + v\cdot \nabla f = g, \quad f(\cdot ,0)= f_0 \quad \text{in}\quad \mathbb{R}^n \] in generalized Campanato spaces $\mathscr{L}^s_{ q(p, N)}(\mathbb{R}^n)$. ... More

Transport equation in generalized Campanato spacesApr 17 2019Apr 18 2019In this paper we study the transport equation in $\mathbb{R}^n \times (0,T)$, $T >0$, \[ \partial _t f + v\cdot \nabla f = g, \quad f(\cdot ,0)= f_0 \quad \text{in}\quad \mathbb{R}^n \] in generalized Campanato spaces $\mathscr{L}^s_{ q(p, N)}(\mathbb{R}^n)$. ... More

On the MGT equation with memory of type IIApr 17 2019We consider the Moore-Gibson-Thompson equation with memory of type II $$ \partial_{ttt} u(t) + \alpha \partial_{tt} u(t) + \beta A \partial_t u(t) + \gamma Au(t)-\int_0^t g(t-s) A \partial_t u(s){\rm d} s=0 $$ where $A$ is a strictly positive selfadjoint ... More

A microscopic derivation of Gibbs measures for nonlinear Schrödinger equations with unbounded interaction potentialsApr 17 2019We study the derivation of the Gibbs measure for the nonlinear Schr\"{o}dinger equation (NLS) from many-body quantum thermal states in the high-temperature limit. In this paper, we consider the nonlocal NLS with defocusing and unbounded $L^p$ interaction ... More

Analysis of Time-domain Electromagnetic Scattering Problem by Multiple CavitiesApr 17 2019Consider the time-domain multiple cavity scattering problem, which arises in diverse scientific areas and has significant industrial and military applications. The multiple cavity embedded in an infinite ground plane, is filled with inhomogeneous media ... More

Identifying variations of magnetic anomalies using geomagnetic monitoringApr 17 2019We are concerned with the inverse problem of identifying magnetic anomalies with varing parameters beneath the Earth using geomagnetic monitoring. Observations of the change in Earth's magnetic field--the secular variation--provide information about the ... More

Boundary layer separation and local behavior for the Steady Prandtl equationApr 17 2019In the case of favorable pressure gradient, Oleinik proved the global existence of classical solution for the 2-D steady Prandtl equation for a class of positive data. In the case of adverse pressure gradient, an important physical phenomena is the boundary ... More

BMO Solvability and Absolute Continuity of Caloric MeasureApr 16 2019We show that BMO-solvability implies scale invariant quantitative absolute continuity (specifically, the weak-$A_\infty$ property) of caloric measure with respect to surface measure, for an open set $\Omega \subset \mathbb{R}^{n+1}$, assuming as a background ... More

Ill posedness for the full Euler system driven by multiplicative white noiseApr 16 2019We consider the Euler system describing the motion of a compressible fluid driven by a multiplicative white noise. We identify a large class of initial data for which the problem is ill posed - there exist infinitely many global in time weak solutions. ... More

Stochastic nonlinear Fokker-Planck equationsApr 16 2019The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with common noise. The ... More

Variational analysis of a two-dimensional frustrated spin system: emergence and rigidity of chirality transitionsApr 16 2019We study the discrete-to-continuum variational limit of the $J_{1}$-$J_{3}$ spin model on the square lattice in the vicinity of the helimagnet/ferromagnet transition point as the lattice spacing vanishes. Carrying out the $\Gamma$-convergence analysis ... More

The Static Maxwell System in Three Dimensional Inhomogeneous Isotropic Media, Generalized Non-Euclidean Modification of the System $(R)$ and Fueter ConstructionApr 16 2019Modified quaternionic analysis in $\mathbb R^3$ was established and successfully developed since 1992 by Leutwiler, Eriksson et al.. The novel approach has led to more general approach of hyperbolic function theory. Some applications are presented now ... More

Reconstruction of piecewise constant layered conductivities in electrical impedance tomographyApr 16 2019This work presents a new constructive uniqueness proof for Calder\'on's inverse problem of electrical impedance tomography, subject to local Cauchy data, for a large class of piecewise constant conductivities that we call "piecewise constant layered conductivities" ... More

Trace operators of the bi-Laplacian and applicationsApr 16 2019We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to describe conformity ... More

An error bound for the slender body approximation of a thin, rigid fiber sedimenting in Stokes flowApr 16 2019We investigate the motion of a thin rigid body in Stokes flow and the corresponding slender body approximation used to model sedimenting fibers. In particular, we derive a rigorous error bound comparing the rigid slender body approximation to the classical ... More

On the entire self-shrinking solutions to Lagrangian mean curvature flow IIApr 16 2019We show Bernstein type results for the entire self-shrinking solutions to Lagrangian mean curvature flow in $(\mathbb{R}^n\times\mathbb{R}^n, g_\tau)$. The proofs rely on a priori estimates and barriers construction.

Some new properties of a suitable weak solution to the Navier-Stokes equationsApr 16 2019The paper is concerned with the IBVP of the Navier-Stokes equations. The goal is the construction of a weak solution enjoying some new properties. Of course, we look for properties which are global in time. The results hold assuming an initial data $v_0 ... More

Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysisApr 16 2019We review and extend the description of ultradifferentiable functions by their almost analytic extensions, i.e., extensions to the complex domain with specific vanishing rate of the $\overline \partial$-derivative near the real domain. We work in a general ... More

Why Are the ARIMA and SARIMA not SufficientApr 16 2019The autoregressive moving average (ARMA) model and its variants like autoregressive integrated moving average (ARIMA), seasonal ARIMA (SARIMA) take the significant position in the time series analysis community. The ARMA model could describe a rational-spectra ... More

Optimal regularity for two-dimensional Pfaffian systems and the fundamental theorem of surface theoryApr 16 2019We prove that a Pfaffian system with coefficients in the critical space $L^2_\mathrm{loc}$ on a simply connected open subset of $\mathbb{R}^2$ has a non-trivial solution in $W^{1,2}_\mathrm{loc}$ if the coefficients are antisymmetric and satisfy a compatibility ... More

On Scales of Sobolev spaces associated to generalized Hardy operatorsApr 16 2019We consider the fractional Laplacian with Hardy potential and study the scale of homogeneous $L^p$ Sobolev spaces generated by this operator. Besides generalized and reversed Hardy inequalities, the analysis relies on a H\"ormander multiplier theorem ... More

Optimal eigenvalue estimates for the Robin Laplacian on Riemannian manifoldsApr 16 2019We consider the first eigenvalue $\lambda_1(\Omega,\sigma)$ of the Laplacian with Robin boundary conditions on a compact Riemannian manifold $\Omega$ with smooth boundary, $\sigma\in\bf R$ being the Robin boundary parameter. When $\sigma>0$ we give a ... More

General Least Gradient Problems with ObstacleApr 16 2019We study existence, structure, uniqueness and regularity of solutions of the obstacle problem \begin{equation*} \inf_{u\in BV_f(\Omega)}\int_{\mathbb{R}^n}\phi(x,Du), \end{equation*} where $BV_f(\Omega)=\{u\in BV(\Omega): u\geq \psi \text{ in }\Omega\text{ ... More

Some Energy Estimates for Stable Solutions to Fractional Allen-Cahn EquationsApr 16 2019In this paper we study stable solutions to the fractional equation \begin{align} (-\Delta)^s u =f(u), \quad |u| < 1 \quad \mbox{in $\mathbb{R}^d$}, \end{align}where $0<s<1$ and $f:[-1,1] \rightarrow \mathbb{R}$ is a $C^{1,\alpha}$ function for $\alpha>\max\{0, ... More

A Note on the Extinction of a Stochastic Differential Equation SIS Epidemic ModelApr 16 2019The aim of this note is to give a new proof to the conjecture, proposed by Gray et al. (2011), on the extinction of a stochastic differential equation SIS epidemic model. The conjecture was proved by Xu (2017). Our proof is much more direct and simpler. ... More

Population dynamics in river networksApr 16 2019Natural rivers connect to each other to form networks. The geometric structure of a river network can significantly influence spatial dynamics of populations in the system. We consider a process-oriented model to describe population dynamics in river ... More

Fractional Laplacian with Hardy drift via desingularizing weightsApr 15 2019We establish the weighted Nash initial estimate for the heat kernel of the fractional Laplacian, perturbed by a drift having a critical-order singularity, using the method of desingularizing weights.

Higher order neck analysis of harmonic maps and its applicationsApr 15 2019In this paper, we prove some refined estimate in the neck region when a sequence of harmonic maps from surfaces blow up. The new estimate allows us to see the shape of the center of the neck region. As an application, we prove an inequality about the ... More

A boundary integral equation approach to computing eigenvalues of the Stokes operatorApr 15 2019The eigenvalues and eigenfunctions of the Stokes operator have been the subject of intense analytical investigation and have applications in the study and simulation of the Navier-Stokes equations. As the Stokes operator is a fourth-order operator, computing ... More

Nodal solutions to a Neumann problem for a class of (p_1,p_2)-Laplacian systemsApr 15 2019Nodal solutions of a parametric (p_1,p_2)-Laplacian system, with Neumann boundary conditions, are obtained by chiefly constructing appropriate sub-super-solution pairs.

Mean value properties of harmonic functions and related topics (a survey)Apr 15 2019Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes of functions. ... More

Blow-up at space infinity for solutions of a system of non-autonomous semilinear heat equationsApr 15 2019In this paper we will see that the global or local existence of solutions to \begin{eqnarray*} \dfrac{\partial u_{1}}{\partial t} & = & \mathit{k}_{1} (t) \Delta u_{1} + h_{1}(t) u_{1}^{p_{11}} u_{2}^{p_{12}},\\ \dfrac{\partial u_{2}}{\partial t} & = ... More

Mathematical analysis of weak and strong solutions to an evolutionary model for magnetoviscoelasticityApr 15 2019The paper is concerned with the analysis of an evolutionary model for magnetoviscoelastic materials in two dimensions. The model consists of a Navier-Stokes system featuring a dependence of the stress tensor on elastic and magnetic terms, a regularized ... More

Study of fractional Poincaré inequalities on unbounded domainsApr 15 2019The central aim of this paper is to study (regional) fractional Poincar\'e type inequalities on unbounded domains satisfying the finite ball condition. Both existence and non existence type results are established depending on various conditions on domains ... More

Existence, multiplicity and regularity for a Schrödinger equation with magnetic potential involving sign-changing weight functionApr 15 2019In this paper we consider the following class of elliptic problems $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\,\, x\in \mathbb{R}^N$$ where $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a sign-changing weight function, ... More

Carleman estimate for an adjoint of a damped beam equation and an application to null controllabilityApr 15 2019In this article we consider a control problem of a linear Euler-Bernoulli damped beam equation with potential in dimension one with periodic boundary conditions. We derive a new Carleman estimate for an adjoint of the equation under consideration. Then ... More

On the radially symmetric traveling waves for the Schr{ö}dinger equation on the Heisenberg groupApr 15 2019We consider radial solutions to the cubic Schr{\"o}dinger equation on the Heisenberg group$$i\partial_t u - \Delta_{\mathbb{H}^1} u = |u|^2u, \quad\Delta_{\mathbb{H}^1} = \frac{1}{4}(\partial_x^2+\partial_y^2) + (x^2+y^2)\partial_s^2, \quad(t,x,y,s) \in ... More

Topics in Applied Mathematics and Nonlinear WavesApr 15 2019The selection of topics in this text has formed the core of a one semester course in applied mathematics at the Arctic University of Norway that has been running continuously since the 1970s. The class has, during its existence, drawn participants from ... More

Reduced Order Modeling for Nonlinear PDE-constrained Optimization using Neural NetworksApr 15 2019Nonlinear model predictive control (NMPC) often requires real-time solution to optimization problems. However, in cases where the mathematical model is of high dimension in the solution space, e.g. for solution of partial differential equations (PDEs), ... More

Global Well-posedness and Long Time Behaviors of Chemotaxis-Fluid System Modeling Coral FertilizationApr 15 2019We consider generalized models on coral broadcast spawning phenomena involving diffusion, advection, chemotaxis, and reactions when egg and sperm densities are different. We prove the global-in-time existence of the regular solutions of the models as ... More

On regularity of the logarithmic forward map of electrical impedance tomographyApr 15 2019This work considers properties of the logarithm of the Neumann-to-Dirichlet boundary map for the conductivity equation in a Lipschitz domain. It is shown that the mapping from the (logarithm of) the conductivity, i.e. the (logarithm of) the coefficient ... More

The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumpsApr 15 2019We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable ... More

Decomposition of generalized O'Hara's energiesApr 15 2019O'Hara introduced several functionals as knot energies. One of them is the M\"{o}bius energy. We know its M\"{o}bius invariance from Doyle-Schramm's cosine formula. It is also known that the M\"{o}bius energy was decomposed into three components keeping ... More

On the completeness of the root functions of the Sturm-Liouville problems for the Lamé system in weighted spacesApr 15 2019We consider three Sturm--Liouville boundary value problems (the coercive ones and the non-coercive one) in a bounded Lipschitz domain for the perturbed Lam\'e operator with the boundary conditions of Robin type. We prove that the problems are Fredholm ... More

An Open Mapping Theorem for the Navier-Stokes EquationsApr 15 2019We consider the Navier-Stokes equations in the layer ${\mathbb R}^n \times [0,T]$ over $\mathbb{R}^n$ with finite $T > 0$. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to ... More

On a mixed problem for the parabolic Lam'e type operatorApr 15 2019We consider a boundary value problem for the parabolic Lam\'e type operator being a linearization of the Navier-Stokes' equations for compressible flow of Newtonian fluids. It consists of recovering a vector-function, satisfying the parabolic Lam\'e type ... More

On the stochastic nonlinear Schrödinger equations at critical regularitiesApr 15 2019We consider the Cauchy problem for the defocusing stochastic nonlinear Schr\"odinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context ... More

Probabilistic local well-posedness of the cubic nonlinear wave equation in negative Sobolev spacesApr 15 2019We study the three-dimensional cubic nonlinear wave equation (NLW) with random initial data below $L^2(\mathbb{T}^3)$. By considering the second order expansion in terms of the random linear solution, we prove almost sure local well-posedness of the renormalized ... More

Time Global Finite-Energy Weak Solutions to the Many-Body Maxwell-Pauli EquationsApr 14 2019We study the quantum mechanical many-body problem of $N$ nonrelativistic electrons interacting with their self-generated classical electromagnetic field and $K$ static nuclei. The system of coupled equations governing the dynamics of the electrons and ... More

Wolff Type Potential Estimates for Stationary Stokes Systems with Dini-BMO CoefficientsApr 14 2019The pointwise gradient estimate for weak solution pairs to the stationary Stokes system with Dini-BMO coefficients is established via the Havin-Maz'ya-Wolff type nonlinear potential of the nonhomogeneous term. In addition, we present a pointwise bound ... More

Multi-d Isothermal Euler Flow: Existence of unbounded radial similarity solutionsApr 13 2019We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity solutions and ... More

Recovery of singularities for the weighted cone transform appearing in the Compton camera imagingApr 13 2019We study the weighted cone transform $I_\kappa$ of distributions with compact support in a domain $M $ of $\mathbb{R}^3$, over cone surfaces whose vertexes are located on a smooth surface away from $M$ and opening angles are limited to an open interval ... More

$Γ$-convergence for functionals depending on vector fields. I. Integral representation and compactnessApr 13 2019Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study functionals depending on $X$. We prove an integral representation for local functionals with respect to $X$ and a result of $\Gamma$-compactness ... More

Existence and multiplicity results for a class of non-linear Schrödinger equations with magnetic potential involving sign-changing non linearityApr 12 2019In this work we consider the following class of elliptic problems $$- \Delta_A u + u = a(x) |u|^{q-2}u+b(x) |u|^{p-2}u , \mbox{ in } \mathbb{R}^N, $$ $u\in H^1_A (\mathbb{R}^N)$, with $2<q<p<2^*= \frac{2N}{N-2}$, $a(x)$ and $b(x)$ are functions that can ... More

Existence at least four solutions for a Schrödinger equation with magnetic potential involving sign-changing weight functionApr 12 2019In this paper we consider the following class of elliptic problems $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,$$ for $x \in \mathbb{R}^N$, $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a sign-changing weight function, ... More

Functionals defined on piecewise rigid functions: Integral representation and $Γ$-convergenceApr 12 2019Apr 15 2019We analyse integral representation and $\Gamma$-convergence properties of functionals defined on \emph{piecewise rigid functions}, i.e., functions which are piecewise affine on a Caccioppoli partition whose derivative in each component is constant and ... More

Existence theory for a time-dependent mean field games model of household wealthApr 12 2019We study a nonlinear system of partial differential equations arising in macroeconomics which utilizes a mean field approximation. This system together with the corresponding data, subject to two moment constraints, is a model for debt and wealth across ... More

Log-gas equilibria with free boundary and optimal transportApr 12 2019Apr 17 2019We study the probability measures $\rho\in \mathcal M(\mathbb R^2)$ minimizing the functional \[ J[\rho]=\iint \log\frac1{|x-y|}d\rho(x)d\rho(y)+d^2(\rho, \rho_0), \] where $\rho_0$ is a given probability measure and $d(\rho, \rho_0)$ is the 2-Wasserstein ... More

Log-gas equilibria with free boundary and optimal transportApr 12 2019We study the probability measures $\rho\in \mathcal M(\mathbb R^2)$ minimizing the functional \[ J[\rho]=\iint \log\frac1{|x-y|}d\rho(x)d\rho(y)+d^2(\rho, \rho_0), \] where $\rho_0$ is a given probability measure and $d(\rho, \rho_0)$ is the 2-Wasserstein ... More

Stability of the Solution Set of Quasi-variational Inequalities and Optimal ControlApr 12 2019For a class of quasivariational inequalities (QVIs) of obstacle-type the stability of its solution set and associated optimal control problems are considered. These optimal control problems are non-standard in the sense that they involve an objective ... More

Sharp Decay Estimates for the Vlasov-Poisson and Vlasov-Yukawa Systems with Small DataApr 12 2019In this paper, we present sharp decay estimates for small data solutions of the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on a modification of the ... More

Surface energy and boundary layers for a chain of atoms at low temperatureApr 12 2019We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ ... More

A new numerical scheme for constrained total variation flows and its convergenceApr 12 2019In this paper, we propose a new numerical scheme for a spatially discrete model of constrained total variation flows, which are total variation flows whose values are constrained in a Riemannian manifold. The difficulty of this problem is that the underlying ... More

Real-time reconstruction of moving point/dipole wave sources from boundary measurementsApr 12 2019This paper is concerned with a reconstruction method for multiple moving point/dipole wave sources. We assume that the number, locations, and magnitudes/moments of wave sources are unknown, and consider the problem to reconstruct these parameters from ... More

On Completeness of Root Functions of Sturm-Liouville Problems with Discontinuous Boundary OperatorsApr 12 2019We consider a Sturm--Liouville boundary value problem in a boun\-ded domain $\cD$ of $\mathbb{R}^n$. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in $\cD$ and the boundary conditions are ... More

On non-coercive mixed problems for parameter-dependent elliptic operatorsApr 12 2019We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of ${\mathbb R}^n$ for a second order parameter-dependent elliptic differential operator $A (x,\partial, \lambda)$ with complex-valued essentially bounded measured ... More

Unique weak solutions of the non-resistive magnetohydrodynamic equations with fractional dissipationApr 12 2019This paper examines the uniqueness of weak solutions to the d-dimensional magnetohydrodynamic (MHD) equations with the fractional dissipation $(-\Delta)^\alpha u$ and without the magnetic diffusion. Important progress has been made on the standard Laplacian ... More

Certain fractional Laplacian equations that do not have smooth solutionsApr 11 2019Let $f$ be a real-valued function defined on $\mathbb{R}$, with $f(0) \neq 0$ and which is not constant in non empty open intervals. We prove the equations \begin{equation}\label{edif} \left\{ \begin{array}{rcll} (-\Delta )^{s}u & = & f(u), & \text{in ... More

External optimal control of fractional parabolic PDEsApr 11 2019In this paper we introduce a new notion of optimal control, or source identification in inverse, problems with fractional parabolic PDEs as constraints. This new notion allows a source/control placement outside the domain where the PDE is fulfilled. We ... More

On the speed rate of convergence of solutions to conservation laws with nonlinear diffusionsApr 11 2019In this paper we analyze the long-time behavior of solutions to conservation laws with nonlinear diffusion terms of different types: saturating dissipation (monotone and non monotone) and singular nonlinear diffusions are considered. In particular, the ... More

The Hénon problem with large exponent in the discApr 11 2019In this paper we consider the H\'enon problem in the unit disc with Dirichlet boundary conditions. We study the asymptotic profile of least energy and nodal least energy radial solutions and then deduce the exact computation of their Morse index for large ... More