# 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

## Abstract

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

${\Delta u+u^q = 0}, in \Omega$

$u=\mu, on \partial \Omega$

, where $1 < q < (N+1) / (N-1)$ and $\mu$ is a Radon measure on $\partial \Omega$. 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