Quantification asymptotique et microlocalisations d'ordre supérieur
Quasilinear problems with singularities.
Rate of approach to a singular steady state in quasilinear reaction-diffusion equations
Real and complex fundamental solutions. A way for unifying mathematical analysis.
Réflexion des singularités analytiques
Réflexion et diffraction des singularités analytiques
Régularité de la solution d'un problème de Cauchy fortement non linéaire à données singulières en un point
Dans cet article, on étudie la régularité d’une solution réelle, appartenant à pour assez grand, d’une équation aux dérivées partielles strictement hyperbolique et fortement non linéaire d’ordre deux. On suppose que les données de Cauchy sur une hypersurface spatiale lisse sont régulières en dehors d’un point, et ont une singularité conormale en ce point; on démontre alors que la réunion des bicaractéristiques nulles issues de ce point est, en dehors de ce point, une hypersurface lisse et...
Régularité Gevrey pour un problème aux limites dans un ouvert à singularité conique
Relativistic hamiltonian dynamics of singularities of the Liouville equation
Removability of singularities with anisotropic growth
With help of suitable anisotropic Minkowski’s contents and Hausdorff measures some results are obtained concerning removability of singularities for solutions of partial differential equations with anisotropic growth in the vicinity of the singular set.
Removable singularities for weak solutions of quasilinear elliptic systems.
Removable singularities in the boundary conditions
Removable singularities of -differential forms and quasiregular mappings.
Removable singularities of solutions of nonlinear singular partial differential equations
1. Introduction. The study of singularities has been one of the main subjects of research in partial differential equations. In the case of linear equations the singularities are now pretty well understood; but in the nonlinear case there seems to be still very few studies. In this paper I want to discuss the singularities of solutions of a class of nonlinear singular partial differential equations in the complex domain. The class is only a model, but it helps one understand that the situation in...
Removable Singularities of Some Strongly Nonlinear Elliptic Equations.
Résultats de régularité, singularité et indice pour l'opérateur de Stokes dans un polygone
Second order parabolic systems, optimal regularity, and singular sets of solutions
Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle
In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches
Semielliptic singularities
Semilinear diffraction of conormal waves (joint work with Melrose and Sa Barreto)