Revista Matemática Iberoamericana


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Volume 16, Issue 3, 2000, pp. 477–513
DOI: 10.4171/RMI/281

Published online: 2000-12-31

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

Marie-Françoise Bidaut-Véron[1] and Laurent Vivier[2]

(1) Université de Tours, France
(2) Université de Toulon et du Var, La Garde, France

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.

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Bidaut-Véron Marie-Françoise, Vivier Laurent: An elliptic semilinear equation with source term involving boundary measures: the subcritical case. Rev. Mat. Iberoam. 16 (2000), 477-513. doi: 10.4171/RMI/281