Semi-groupes de Feller invariants sur les espaces hyperboliques
Semi-polar sets are almost negligible.
Silov Boundaries of Spaces of Functions with Noncompact Domains.
Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Some Dirichlet spaces obtained by subordinate reflected diffusions.
In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
Some properties and applications of harmonic mappings
Some properties of composition operators on the Dirichlet space.
Strong uniqueness for certain infinite dimensional Dirichlet operators and applications to stochastic quantization
Suites définies négatives et espaces de Dirichlet sur la sphère
Sur la représentation des formes de Dirichlet
On montre qu’une forme de Dirichlet est décomposable de manière unique en deux formes intégrales et une forme locale. On indique l’expression de cette partie locale dans un cas régulier.
Sur la théorie du potentiel dans les domaines de John.
Using rather elementary and direct methods, we first recover and add on some results of Aikawa-Hirata-Lundh about the Martin boundary of a John domain. In particular we answer a question raised by these authors. Some applications are given and the case of more general second order elliptic operators is also investigated. In the last parts of the paper two potential theoretic results are shown in the framework of uniform domains or the framework of hyperbolic manifolds.
Sur une question de H. Brezis, M. Marcus et A. C. Ponce
Symmetric reflected diffusions