An elliptic semilinear equation with source term involving boundary measures: the subcritical case
Marie‐Françoise Bidaut‐Véron, Laurent Vivier · Revista Matemática Iberoamericana · 2000
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 ), \begin{cases}{\Delta u+u^q = 0}, &\text{in }\Omega,\\u=\mu, &\text{on }\partial \Omega,\end{cases} 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.