Existence and regularity results for nonlinear elliptic equations with measure data

Abstract

In this paper we prove some existence and regularity results for equations of the type $- \text{div}\, (a(u,u,\Delta u)+ K(x,u)) +H(x,\Delta u) =f $, in a bounded open set $\Omega$, $u=0 $ on $ \partial \Omega$, where $a$, $K$ and $H$ are Caratheodory functions and $f$ is a Radon measure.