A tauberian theorem in quantum mechanical inverse scattering theory
A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal residual method with a measure of the residual corresponding to the error in a specified solution norm. The residual norm can be designed such that the resulting low-rank approximations are optimal with respect to particular norms of interest, thus allowing to take...
A Theorem on Elliptic Differential Inequalities with an Application to Gradient Bounds.
A theorem on "localized" self-adjointness of Schrödinger operators with potentials.
A topological asymptotic analysis for the regularized grey-level image classification problem
The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.
A trace formula for resonances and application to semi-classical Schrödinger operators
On décrit une formule de trace [S] pour les résonances, qui est valable en toute dimension et pour les perturbations à longue portée du Laplacien. On établit une nouvelle application à l’éxistence de nombreuses résonances pour des opérateurs de Schrödinger semi-classiques.
A two parameters Ambrosetti-Prodi problem.
A Two-Particle Quantum System with Zero-Range Interaction
We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.
A two-step Monge-Ampère procedure for solving a fourth order PDE for affine hypersurfaces with constant curvature.
A unified approach to a posteriori error estimation using element residual methods.
A uniform boundary Harnack inequality on non-tangentially accessible domains.
A uniformly accurate finite volume discretization for a convection-diffusion problem.
A unique continuation property for linear elliptic systems and nonresonance problems.
A uniqueness result for an inverse problem
We establish a uniqueness result for an overdetermined boundary value problem. We also raise a new question.
A uniqueness theorem for higher order elliptic partial differential equations.
A Uniqueness Theorem for Some Nonlinear Boundary Value Problems with a Large Parameter.
A variational analysis of a gauged nonlinear Schrödinger equation
This paper is motivated by a gauged Schrödinger equation in dimension 2 including the so-called Chern-Simons term. The study of radial stationary states leads to the nonlocal problem: , where . This problem is the Euler-Lagrange equation of a certain energy functional. In this paper the study of the global behavior of such functional is completed. We show that for , the functional may be bounded from below or not, depending on . Quite surprisingly, the threshold value for is explicit. From...
A variational approach in weighted Sobolev spaces to the operator - ... + .../... X1 in exterior domains of IR3.
A Variational Approach to Bifurcation in Lp on an Unbounded Symmetrical Domain.
A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
We consider a simple reaction-diffusion system exhibiting Turing's diffusion driven instability if supplemented with classical homogeneous mixed boundary conditions. We consider the case when the Neumann boundary condition is replaced by a unilateral condition of Signorini type on a part of the boundary and show the existence and location of bifurcation of stationary spatially non-homogeneous solutions. The nonsymmetric problem is reformulated as a single variational inequality with a potential...