Opérateurs différentiels hypoelliptiques et groupes nilpotents
Opérateurs hypoelliptiques sur des groupes nilpotents
Operatori differenziali a coefficienti costanti di tipo iperbolico-(ipo)ellittico
Parabolic equations relative to vector fields.
Perturbative methods in scales of Banach spaces: applications for Gevrey regularity of solutions to semilinear partial differential equations.
Power Series Spaces and Weighted Solution Spaces of Partial Differential Equations.
Quasielliptic operators and Sobolev type equations.
Quelques résultats d’hypocoercitivité en théorie cinétique collisionnelle
Nous présentons une introduction à un nouveau champ de recherche, l’hypocoercitivité. Nous énonçons quelques résultats obtenus récemment avec différents co-auteurs (Lukas Neumann, Jean Dolbeault, Christian Schmeiser) dans le cas des équations cinétiques collisionnelles, en particulier pour les équations de type Boltzmann. Puis nous présentons quelques perspectives de recherche à plus long terme, dans le but de dégager une théorie unifiée de l’hypocoercitivité en théorie cinétique collisionnelle.
Randverteilungen von Nullösungen hypoelliptischer Differentialgleichungen.
Régularité Gevrey pour les opérateurs de Hörmander
Régularité optimale des solutions de systèmes différentiels et du Laplacien associé; application au ....b.
Régularité pour des systèmes à coefficients constants
Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
We prove the hypoellipticity for systems of Hörmander type with constant coefficients in Carnot groups of step 2. This result is used to implement blow-up methods and prove partial regularity for local minimizers of non-convex functionals, and for solutions of non-linear systems which appear in the study of non-isotropic metric structures with scalings. We also establish estimates of the Hausdorff dimension of the singular set.
Remarks on Gårding inequalities for differential operators
Classical Gårding inequalities such as those of Hörmander, Hörmander-Melin or Fefferman-Phong are proved by pseudo-differential methods which do not allow to keep a good control on the supports of the functions under study nor on the smoothness of the coefficients of the operator. In this paper, we show by very simple calculations that in certain special situations, the results that can be obtained directly are much better than those expected thanks to the general theory.
Riesz means for the eigenfunction expansions for a class of hypo-elliptic differential operators
We study the Riesz means for the eigenfunction expansions of a class of hypoelliptic differential operators on the Heisenberg group. The operators we consider are homogeneous with respect to dilations and invariant under the action of the unitary group. We obtain convergence results in norm, at Lebesgue points and almost everywhere. We also prove localization results.
Risolubilità e ipoellitticità per equazioni differenziali a derivate parziali semilineari con caratteristiche multiple
Schrödinger equation on the Heisenberg group
Solvability of invariant sublaplacians on spheres and group contractions
In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians on the spheres . In the second part, we introduce a larger family of left-invariant sublaplacians on and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.
Some Examples of Hypoelliptic Partial Differential Equations.
Some Hardy type inequalities in the Heisenberg group.