On functions with bounded mixed variance
On integrals of harmonic functions over annuli.
On Lipschitz continuity of harmonic quasiregular maps on the unit ball in .
On the Boundary Behaviour of the Perron Generalized Solution.
On the boundary limits of harmonic functions with gradient in
This paper deals with tangential boundary behaviors of harmonic functions with gradient in Lebesgue classes. Our aim is to extend a recent result of Cruzeiro (C.R.A.S., Paris, 294 (1982), 71–74), concerning tangential boundary limits of harmonic functions with gradient in , denoting the upper half space of the -dimensional euclidean space . Our method used here is different from that of Nagel, Rudin and Shapiro (Ann. of Math., 116 (1982), 331–360); in fact, we use the integral representation...
On the boundary values of harmonic functions.
Over the years many methods have been discovered to prove the existence of a solution of the Dirichlet problem for Laplace's equation. A fairly recent collection of proofs is based on representations of the Green's functions in terms of the Bergman kernel function or some equivalent linear operator [3]. Perhaps the most fundamental of these approaches involves the projection of an arbitrary function onto the class of harmonic functions in a Hilbert space whose norm is defined by the Dirichlet integral...
On the existence of weighted boundary limits of harmonic functions
We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
On weighed spaces
Parabolic measure on domains of class Lip
Perturbation theory for nonlinear Dirichlet problems.
Poisson Integrals and Boundary Components of Symmetric Spaces.
Poisson kernel characterization of Reifenberg flat chord arc domains
Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.
Quasiadditivity of capacity and minimal thinness.
Rectilinearly and rectifiably ambiguous points of a function harmonic inside a sphere
Regularizing sets of irregular points.
Relative Fatou theorem for harmonic functions of rotation invariant stable processes in smooth domains
For domains we give exact asymptotics near the domain’s boundary for the Green function and Martin kernel of the rotation invariant α-stable Lévy process. We also obtain a relative Fatou theorem for harmonic functions of the stable process.
Restricted mean value property in axiomatic potential theory
Solutions positives et mesure harmonique pour des opérateurs paraboliques dans des ouverts «lipschitziens»
Soit un opérateur parabolique sur écrit sous forme divergence et à coefficients lipschitziens relativement à une métrique adaptée. Nous cherchons à comparer près de la frontière le comportement relatif des -solutions positives sur un domaine “lipschitzien”. Dans un premier temps, nous démontrons un principe de Harnack uniforme pour certaines -solutions positives. Ce principe nous permet alors de démontrer une inégalité de Harnack forte à la frontière pour certains couples de -solutions positives....
Tangential limits of monotone Sobolev functions.