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 .