JournalszaaVol. 18, No. 3pp. 539–555

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

  • Carsten Ebmeyer

    Universität Bonn, Germany
Mixed Boundary Value Problems for Nonlinear Elliptic Systems in n-Dimensional Lipschitzian Domains cover
Download PDF

Abstract

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

i=1niFi(x,u)=f(x)+i=1nifi(x),– \sum^n_{i=1} \partial_i F_i (x, \triangledown u) = f(x) + \sum^n_{i=1} \partial_i f_i (x),

where ΩRn\Omega \in \mathbb R^n is a bounded domain with a piecewise smooth boundary (e.g., Ω\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 [Ws,2(Ω)]N[W^{s, 2} (\Omega)]^N-regularity (s<32)(s < \frac{3}{2}) of uu.

Cite this article

Carsten Ebmeyer, Mixed Boundary Value Problems for Nonlinear Elliptic Systems in n-Dimensional Lipschitzian Domains. Z. Anal. Anwend. 18 (1999), no. 3, pp. 539–555

DOI 10.4171/ZAA/897