Mixed boundary value problems for nonlinear elliptic equations with $p$-structure in nonsmooth domains

Abstract

Nonlinear partial differential equations with $p$--structure for $1 <p <\infty$ are investigated under mixed boundary value conditions on $n$-dimensional domains with a piecewise-smooth boundary. $L^q(\Omega)$--properties of the first derivatives of weak solutions in Sobolev and in Morrey spaces are proven.