Positive quasi-minima
Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains.
Positive solutions of nonlinear elliptic systems
We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.
Prescribing a fourth order conformal invariant on the standard sphere, part II : blow up analysis and applications
In this paper we perform a fine blow up analysis for a fourth order elliptic equation involving critical Sobolev exponent, related to the prescription of some conformal invariant on the standard sphere . We derive from this analysis some a priori estimates in dimension and . On these a priori estimates, combined with the perturbation result in the first part of the present work, allow us to obtain some existence result using a continuity method. On we prove the existence of at least one...
Problèmes aux limites elliptiques dans des ouverts non bornés
Problèmes de Cauchy hyperboliques en dimension infinie
Problèmes de Cauchy pour des opérateurs singuliers
Problèmes elliptiques du second ordre sur une variété euclidienne à l'infini
Problèmes mixtes hyperboliques
Profile decomposition for solutions of the Navier-Stokes equations
We consider sequences of solutions of the Navier-Stokes equations in , associated with sequences of initial data bounded in . We prove, in the spirit of the work of H.Bahouri and P.Gérard (in the case of the wave equation), that they can be decomposed into a sum of orthogonal profiles, bounded in , up to a remainder term small in ; the method is based on the proof of a similar result for the heat equation, followed by a perturbation–type argument. If is an “admissible” space (in particular ...
Prolongement à la frontière des solutions du problème des dérivées obliques
Propagation de singularités pour des équations hyperboliques non linéaires
Propagation of space moments in the Vlasov-Poisson equation and further results
Properties of normal boundary problems for elliptic even-order systems
Propriété des itérés et ellipticité
Propriétés de certaines solutions d'inégalité aux dérivées partielles de type parabolique
Propriétés de moyenne pour les solutions de systèmes elliptiques
In this article, we consider the set F of functions annihilated by a uniformly elliptic system S in an open set Ω of Rn.We show that, as in the case of harmonic functions, F satisfies a submean-property, first for p=2 by elliptic estimates, then for all p > 0:|∇k u(x)|p ≤ C / (rn+kp) ∫B(x,r) |u(y)|p dyfor each u in F, each k > 0 and every ball B(x,r) included in Ω.As a consequence, we can compare ||u||Lp(Ω) and ||∇ku||Lp(Ω,δkp) where δ is the distance to the boundary of Ω, under the...
Propriétés des courbes intégrales de champs de vecteurs et estimations ponctuelles d'équation elliptiques dégénérés
Pseudo-differential operators with positive symbols
Pseudo-spectrum for a class of semi-classical operators
We study in this paper a notion of pseudo-spectrum in the semi-classical setting called injectivity pseudo-spectrum. The injectivity pseudo-spectrum is a subset of points in the complex plane where there exist some quasi-modes with a precise rate of decay. For that reason, these values can be considered as some ‘almost eigenvalues’ in the semi-classical limit. We are interested here in studying the absence of injectivity pseudo-spectrum, which is characterized by a global a priori estimate. We prove...