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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 3, 1999, pp. 539–555
DOI: 10.4171/ZAA/897

Published online: 1999-09-30

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

Carsten Ebmeyer[1]

(1) Universität Bonn, Germany

Let $u : \Omega \to \mathbb R^n$ be the solution of the nonlinear elliptic system $$– \sum^n_{i=1} \partial_i F_i (x, \triangledown u) = f(x) + \sum^n_{i=1} \partial_i f_i (x),$$ 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 $u$.

Keywords: Mixed boundary value problems, piecewise smooth boundaries, Nikolskii spaces

Ebmeyer Carsten: Mixed Boundary Value Problems for Nonlinear Elliptic Systems in n-Dimensional Lipschitzian Domains. Z. Anal. Anwend. 18 (1999), 539-555. doi: 10.4171/ZAA/897