Homogeneous estimates for oscillatory integrals.
Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue...
Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation
In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed....
Hypoelliptic estimates for some linear diffusive kinetic equations
This note is an announcement of a forthcoming paper [13] in collaboration with K. Pravda-Starov on global hypoelliptic estimates for Fokker-Planck and linear Landau-type operators. Linear Landau-type equations are a class of inhomogeneous kinetic equations with anisotropic diffusion whose study is motivated by the linearization of the Landau equation near the Maxwellian distribution. By introducing a microlocal method by multiplier which can be adapted to various hypoelliptic kinetic equations,...
Hypoellipticité d'équations aux dérivées partielles non linéaires
Inégalités de résolvante pour l’opérateur de Schrödinger avec potentiel multipolaire critique
On étudie un opérateur de la forme sur , où est un potentiel admettant plusieurs pôles en . Plus précisément, on démontre l’estimation de résolvante tronquée à hautes fréquences, classique dans les cas non-captifs, et qui implique l’effet régularisant standard pour l’équation de Schrödinger correspondante. La preuve est basée sur l’introduction d’une mesure de défaut micro-locale semi-classique. On démontre également, dans le même contexte, des inégalités de Strichartz pour l’équation de Schrödinger....
Infinity Laplace equation with non-trivial right-hand side.
Inhomogeneous parabolic Neumann problems
Second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions are studied. Existence and uniqueness of weak solutions and their continuity up to the boundary of the parabolic cylinder are proved using methods from the theory of integrated semigroups, showing in particular the well-posedness of the abstract Cauchy problem in spaces of continuous functions. Under natural assumptions on the coefficients and the inhomogeneity the...
Initial boundary value problem for generalized Zakharov equations
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.
Initial traces of solutions to a one-phase Stefan problem in an infinite strip.
The main result of this paper is an integral estimate valid for non-negative solutions (with no reference to initial data) u ∈ L1loc (Rn x (0,T)) to(0.1) ut - Δ(u - 1)+ = 0, in D'(Rn x (0,T)),for T > 0, n ≥ 1. Equation (0.1) is a formulation of a one-phase Stefan problem: in this connection u is the enthalpy, (u - 1)+ the temperature, and u = 1 the critical temperature of change of phase. Our estimate may be written in the form(0.2) ∫Rn u(x,t) e-|x|2 / (2 (T - t)) dx ≤ C, 0 <...
Integrability of derivations of classical solutions of Dirichlet's problem for an elliptic equation.
Integral inequalities and summability of solutions of some differential problems
The aim of this note is to indicate how inequalities concerning the integral of on the subsets where |u(x)| is greater than k () can be used in order to prove summability properties of u (joint work with Daniela Giachetti). This method was introduced by Ennio De Giorgi and Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems. In some joint works with Thierry Gallouet, inequalities concerning the integral of on the subsets where |u(x)| is less than k () or...
Interaction des singularités pour les équations aux dérivées partielles non linéaires
Interaction of progressing waves through a nonlinear potential
Interface and mixed boundary value problems on -dimensional polyhedral domains.
Interior gradient estimates for nonuniformly parabolic equations. II.
Interior regularity for the quasilinear elliptic systems with nonsmooth coefficients