Mixed Boundary Value Problems for Nonlinear Elliptic Systems in n-Dimensional Lipschitzian Domains

Abstract

Let $u:\Omega \to {\mathbb{R}}^n$ be the solution of the nonlinear elliptic system

where $\Omega \in {\mathbb{R}}^n$ is a bounded domain with a piecewise smooth boundary (e.g., $\Omega$ is a polyhedron). It is assumed that a mixed boundary value condition is given. Global regularity results in Sobolev and in Nikolskii spaces are proven, in particular $[W^{s,2}(\Omega ){]}^N$-regularity $(s<\frac{3}{2})$ of $u$.