Boundary continuity for quasiminimizers on metric spaces
type: Item
instance of: scholarly article
title: Boundary continuity for quasiminimizers on metric spaces
zbMATH Open document ID: 1026.49029
author: Jana Björn
published in: Illinois Journal of Mathematics
publication date: 2003-01-01T00:00:00Z
review text: The paper considers a generalization of the variational problem \[ \int_\Omega|\nabla u(x)|^p dx\to\min,\quad u\in W^{1,p}_0(\Omega)+ w, \] on Sobolev type spaces on metric measure spaces [see, e.g., \textit{B. Franchi}, \textit{P. Hajlasz} and \textit{P. Koskela}, ``Definition of Sobolev classes on metric spaces'', Ann. Inst. Fourier 49, 1903-1924 (1999; Zbl 0938.46037)], and gives some sufficient conditions for boundary continuity (Hölder continuity) of quasiminimizers.
Mathematics Subject Classification ID: 49N60
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 58E35
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1839951
zbMATH Keywords: \(p\)-energy
zbMATH Keywords: boundary regularity
zbMATH Keywords: Hölder continuity
zbMATH Keywords: metric measure spaces
zbMATH Keywords: boundary continuity
zbMATH Keywords: quasiminimizers
reviewed by: Uldis Raitums
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1839951