Existence and stability of solutions of general semilinear elliptic equations with measure data
Laurent Véron · arXiv (Cornell University) · 2012
We study existence and stability for solutions of $Lu+g(x; u) = \\omega$ in the closure of open set $\\Omega$ where L is a second order elliptic operator, $g$ a Caratheodory function and $\\omega$ a measure in $\\bar\\Omega$. We present a uni ed theory of the Dirichlet problem and the Poisson equation. We prove the stability of the problem with respect to weak convergence of the data.