L2-Integrability of Second Order Derivatives for Poisson's Equation in Nonsmooth Domains.
La convolution dans faible de
La quasi-continuité dans l'étude du problème de Dirichlet. Effilement minimal abstrait et ensembles convexes compacts
Les problèmes de Dirichlet sur la frontière de Martin, sur la frontière de Choquet d’un simplexe métrisable compact, et sur la frontière de Silov d’un simplexe de Bauer métrisable sont tous susceptibles d’une seule méthode de résolution qui utilise un espace de fonctions dites quasi-continues. Cela contient aussi le théorème des limites fines de Fatou-Naïm qui exprime une quasi-continuité jusqu’à la frontière.
Landau's theorem for p-harmonic mappings in several variables
A 2p-times continuously differentiable complex-valued function f = u + iv in a domain D ⊆ ℂ is p-harmonic if f satisfies the p-harmonic equation , where p (≥ 1) is a positive integer and Δ represents the complex Laplacian operator. If Ω ⊂ ℂⁿ is a domain, then a function is said to be p-harmonic in Ω if each component function (i∈ 1,...,m) of is p-harmonic with respect to each variable separately. In this paper, we prove Landau and Bloch’s theorem for a class of p-harmonic mappings f from...
Layer potentials C*-algebras of domains with conical points
To a domain with conical points Ω, we associate a natural C*-algebra that is motivated by the study of boundary value problems on Ω, especially using the method of layer potentials. In two dimensions, we allow Ω to be a domain with ramified cracks. We construct an explicit groupoid associated to ∂Ω and use the theory of pseudodifferential operators on groupoids and its representations to obtain our layer potentials C*-algebra. We study its structure, compute the associated K-groups, and prove Fredholm...
Layer potentials on boundaries with corners and edges
Le compactifié de Martin d’un domaine Lipschitzien borné dans
L...-estimates for Green potentials in Lipschitz domains.
Level sets of polynomials in several real variables.
Lewy's theorem fails in higher dimensions.
Limites de quotients de fonctions harmoniques et espaces de Hardy associés à une marche aléatoire sur un groupe abélien
Lindelöf theorems for monotone Sobolev functions.
Linéarisation de la notion de convexité par rapport à un ensemble de fonctions
Liouville type theorems for mappings with bounded (co)-distortion
We obtain Liouville type theorems for mappings with bounded -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded -codistorsion.
Liouville type theorems for φ-subharmonic functions.
In this paper we present some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. Phragmen-Lindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed.
Liouville's theorem and the restricted mean property for biharmonic functions.
Lipschitz conditions on the modulus of a harmonic function.
Littlewood-Paley type inequalities for -harmonic functions.
Littlewood-Paley Type Inequalities for M-harmonic Functions
Littlewood-Paley-Stein theory on Cn and Weyl multipliers.