Semilinear elliptic equations and systems with measure data: existence and a priori estimates
Marie Françoise Bidaut-Véron, Cecilia S. Yarur · Advances in Differential Equations · 2002
We give existence results and a priori estimates for a semilinear elliptic problem of the form \begin{equation*} \left\{ \begin{array}{l} -\Delta w=w^{Q}+\mu ,\qquad \text{in \thinspace }\Omega , \\ w=\lambda ,\qquad \qquad \qquad \quad \text{on }\partial \Omega , \end{array} \right. \end{equation*} where $Q>0,$ and $\mu $ and $\lambda $ are nonnegative Radon measures in $ \Omega $ and $\partial \Omega ,$ with $\int_{\Omega }\rho \,d\mu 0,$ and the same assumptions on $\eta $ and $\kappa .$