JournalsrmiVol. 16, No. 3pp. 477–513

An elliptic semilinear equation with source term involving boundary measures: the subcritical case

  • Marie-Françoise Bidaut-Véron

    Université de Tours, France
  • Laurent Vivier

    Université de Toulon et du Var, La Garde, France
An elliptic semilinear equation with source term involving boundary measures: the subcritical case cover

Abstract

We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain Ω\Omega of RN(N2)\mathbb R^N (N≥2),

Δu+uq=0,inΩ{\Delta u+u^q = 0}, in \Omega
u=μ,onΩu=\mu, on \partial \Omega

, where 1<q<(N+1)/(N1)1 < q < (N+1) / (N-1) and μ\mu is a Radon measure on Ω\partial \Omega. We give a priori estimates and existence results. They lie on the study of the superharmonic functions in some weighted Marcinkiewicz spaces.

Cite this article

Marie-Françoise Bidaut-Véron, Laurent Vivier, An elliptic semilinear equation with source term involving boundary measures: the subcritical case. Rev. Mat. Iberoam. 16 (2000), no. 3, pp. 477–513

DOI 10.4171/RMI/281