Mixed boundary value problems for nonlinear elliptic systems in \(n\)-dimensional Lipschitzian domains
type: Item
instance of: scholarly article
title: Mixed boundary value problems for nonlinear elliptic systems in \(n\)-dimensional Lipschitzian domains
zbMATH Open document ID: 0931.35045
DOI: 10.4171/ZAA/897
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2000-02-23T00:00:00Z
full work available at URL: https://eudml.org/doc/48330
review text: 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 \(u\).
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1356394
zbMATH Keywords: piecewise smooth boundaries
zbMATH Keywords: Nikolskii spaces
author: C. Ebmeyer
MaRDI profile type: Publication
cites work: Q4073917
cites work: On Asymptotics of Solutions of Elliptic Mixed Boundary Value Problems of Second-Order in Domains with Vanishing Edges
cites work: A COUNTEREXAMPLE IN THE THEORY OF MIXED BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATIONS IN NON-SMOOTH DOMAINS
cites work: On mixed boundary value problems of Dirichlet oblique-derivative type in plane domains with piecewise differentiable boundary
cites work: Q4007564
cites work: Behavior of solutions of the Dirichlet problem for a second-order quasilinear elliptic equation of general form close to a corner point
cites work: Elliptic boundary value problems on corner domains. Smoothness and asymptotics of solutions
cites work: Mixed boundary value problems for nonlinear elliptic equations in multidimensional non-smooth domains
cites work: Q3470840
cites work: Edge Behavior of the Solution of an Elliptic Problem
cites work: Q5589570
cites work: Linear and quasilinear elliptic equations
cites work: On the behaviour of solutions to the Dirichlet problem for second order elliptic equations near edges and polyhedral vertices with critical angles
cites work: Asymptotic Expansions of Solutions of the Dirichlet Problem for Quasilinear Elliptic Equations of Second Order Near a Conical Point
cites work: Q5518064
cites work: Decompositions in Edge and Corner Singularities for the Solution of the Dirichlet Problem of the Laplacian in a Polyhedron
description: scientific article; zbMATH DE number 1356394