Behavior of the solution of the Zaremba problem near a singular point of the boundary
type: Item
instance of: scholarly article
title: Behavior of the solution of the Zaremba problem near a singular point of the boundary
zbMATH Open document ID: 0612.35057
DOI: 10.1007/BF01158409
author: T. M. Kerimov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Es seien \(G\subset {\mathbb{R}}^ n\), \(n>2\), mit dem Rand \(\Gamma\), \(F\subset \Gamma\) mit positiver Wiener-Kapazität und \({\mathcal L}u:=-\sum (a_{ij}(x)u_{x_ j})_{x_ i}\) ein elliptischer Operator mit reellen meßbaren Koeffizienten. Der Verf. untersucht in der vorliegenden Note das Randverhalten der Lösungen von \({\mathcal L}u=f\) mit \(u| F=0\) und \(\partial u/\partial n|_{\Gamma \setminus F}=0\) und zeigt für eine Klasse von ''Spitzen'' \(0\in F\) mit Kapazitätsmethoden die Stetigkeit der Lösungen in 0.
reviewed by: Rolf Leis
Mathematics Subject Classification ID: 35J67
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 3989919
zbMATH Keywords: positive Wiener capacity
zbMATH Keywords: real measurable coefficient
zbMATH Keywords: boundary behavior
zbMATH Keywords: continuity
MaRDI profile type: Publication
cites work: Q3934843
cites work: Solvability of a first order linear partial differential equation
cites work: A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
description: scientific article; zbMATH DE number 3989919