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)
Semilinear hyperbolic systems in one space dimension with strongly singular initial data.
Singular dynamics for semiconcave functions
Singular -harmonic functions and related quasilinear equations on manifolds.
Singular solutions of the Briot-Bouquet type partial differential equations
Singular solutions to Protter's problem for the 3-D wave equation involving lower order terms.
Singularités des problèmes aux limites dans des polyèdres
Singularités éliminables pour des équations semi-linéaires
Étant donné un opérateur différentiel d’ordre sur un ouvert de , un compact de , et , nous montrons que toute solution de “ sur ” est solution de “ sur ” dès que la -capacité de est nulle. Cette condition s’avère nécessaire quand est un opérateur elliptique d’ordre 2. Dans ce cas, nous montrons aussi que où est une mesure de Radon bornée sur , a une solution si et seulement si ne charge pas les ensembles de -capacité nulle.
Singularités isotropes des solutions d'équations elliptiques non linéaires
Singularities of Elliptic Equations with an Exponential Nonlinearity.
Singularities of Maxwell’s system in non-hilbertian Sobolev spaces
We study the regularity of the solution of the regularized electric Maxwell problem in a polygonal domain with data in . Using a duality method, we prove a decomposition of the solution into a regular part in the non-Hilbertian Sobolev space and an explicit singular one.
Smooth singular solutions of hyperplane fields. I
Smooth singular solutions of hyperplane fields. II
Solutions analytiques des équations aux dérivées partielles à coefficients constants
Solutions of the equation
Some exact estimates of weak solutions to a mixed boundary value problem for nonlinear equations in domains with nonsmooth boundary.
Sulle singolarità delle soluzioni di un problema di Dirichlet per un'equazione iperbolica del secondo ordine
A solution of a particular Dirichlet problem for a non-linear 2nd order hyperbolic equation is regular at any point of the boundary but one point. The kind of singularity which exhibits at this point is investigated.