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

Abstract

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

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.