Mixed boundary value problems for nonlinear elliptic systems in \(n\)-dimensional Lipschitzian domains
Summary: Let \(u:\Omega \to\mathbb{R}^N\) be the solution of the nonlinear elliptic system \[ -\sum^n_{i=1} \partial_iF_i(x,\nabla u)=f(x)+ \sum^n_{i=1} \partial_i f_i(x), \] where \(\Omega\subset \mathbb{R}^n\) 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 \((s< {3\over 2})\) of \(u\).
scientific article; zbMATH DE number 1356394
scientific article