An application of Bergman-Whittaker operator
An Approximation Theorem for Integrable Harmonic Vector Fields.
An elliptic semilinear equation with source term involving boundary measures: the subcritical case.
We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω of RN (N ≥ 2),⎧ Δu + uq = 0, in Ω⎨⎩ u = μ, on ∂Ωwhere 1 < q < (N + 1)/(N - 1) and μ is a Radon measure on ∂Ω. We give a priori estimates and existence results. The lie on the study of superharmonic functions in some weighted Marcinkiewicz spaces.
An example concerning the topological character of the zero-set of a harmonic function.
An example related to boundedness of subharmonic functions
An extension theorem for supertemperatures.
Analogies entre espaces hyperboliques réels et l’arbre de Bruhat-Tits sur
Analysis on local Dirichlet spaces. I. Recurrence, conservativeness and Lp-Liouville properties.
Analytic continuation for some classes of separately analytic functions of real variables
For functions that are separately solutions of an elliptic homogeneous PDE with constant coefficients, we prove an analogue of Siciak's theorem for separately holomorphic functions.
Approximation by Solutions of Elliptic Equations on Closed Subsets of Euclidean Space.
Approximation des fonctions harmoniques à l'aide d'un théorème de G. F. Vincent-Smith
Approximation of harmonic functions
Let be harmonic in a bounded domain with smooth boundary. We prove that if the boundary values of belong to , where and denotes the surface measure of , then it is possible to approximate uniformly by function of bounded variation. An example is given that shows that this result does not extend to .
Bases communes dans certains espaces de fonctions harmoniques et fonctions séparément harmoniques sur certains ensembles de
Bernstein Theorems for Harmonic Morphisms from R3 and S3.
Boundaries of graphs of harmonic functions.
Boundary behaviour of positive harmonic functions on Lipschitz domains.
Boundary limits of Green's potentials along curves II. Lipschitz domains
Boundary Value Characterizations for Weighted Hardy Spaces of Harmonic Functions.
Boundary values of harmonic functions in mixed norm spaces and their atomic structure
Brownian motion and generalized analytic and inner functions
Let be a mapping from an open set in into , with . To say that preserves Brownian motion, up to a random change of clock, means that is harmonic and that its tangent linear mapping in proportional to a co-isometry. In the case , , such conditions signify that corresponds to an analytic function of one complex variable. We study, essentially that case , , in which we prove in particular that such a mapping cannot be “inner” if it is not trivial. A similar result for , would solve...