Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 3, pp. 539555 (1999) 

Mixed Boundary Value Problems for Nonlinear Elliptic Systems in $n$Dimensional Lipschitzian DomainsC. EbmeyerUniversität Bonn, Mathematisches Seminar, Nußallee 15, D  53115 BonnAbstract: Let $u: \Omega \to \R^N$ be the solution of the nonlinear elliptic system $$ \sum_{i=1}^n \partial_iF_i(x,\nabla u)=f(x)+\sum_{i=1}^n\partial_if_i(x), $$ where $\Omega \subset \R^n$ 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 \ \ $(s < {3 \over 2})$ of $u$. Keywords: mixed boundary value problems, piecewise smooth boundaries, Nikolskii spaces Classification (MSC2000): 35J55, 35J65, 35J25 Full text of the article:
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