Nonlinear Elliptic Problems Under Mixed Boundary Value Conditions in Nonsmooth Domains

Abstract

%\noindent Strongly nonlinear elliptic equations and systems are investigated under mixed boundary value conditions. It is supposed that the domain is a multidimensional polyhedral domain. Global regularity results of $|\nabla u|^{\sigma}$ $(\sigma\geq 1)$ are proven, in particular, $W^{s,p}(\Omega)$-regularity $(s<\frac{1}{2})$ of $|\nabla u|$ and $|\nabla u|^2$.