Characterization for the Kuratowski limits of a sequence of Sobolev spaces
type: Item
instance of: scholarly article
title: Characterization for the Kuratowski limits of a sequence of Sobolev spaces
zbMATH Open document ID: 0924.46028
author: Dorin Bucur
published in: Journal of Differential Equations
publication date: 1999-11-11T00:00:00Z
review text: Let \(B\) be the unit ball in \(\mathbb{R}^n\), \(\{\Omega_j\}^\infty_{j=1}\subset B\) and \(\Omega\subset B\) be domains. The author studies the Kuratowski-Mosco limits \[ \{u\in\mathring W^1_p(B): \exists u_j\in \mathring W^1_p(\Omega_j),u_j\to u\}, \] \[ \{u\in\mathring W^1_p(B): \exists u_{j_k}\in \mathring W^1_p(\Omega_{j_k}), u_{j_k}\to u\}, \] where \(\mathring W^1_p\) are the usual Sobolev spaces, \(1< p<\infty\). The convergence is in \(\mathring W^1_p(B)\). Criteria are formulated in terms of capacity. Applications to the continuity behaviour of solutions of the Dirichlet problem for the \(p\)-Laplacian are given.
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1271362
zbMATH Keywords: Kuratowski-Mosco limits
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: capacity
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: \(p\)-Laplacian
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3497
OpenAlex ID: W1977084157
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DOI: 10.1006/JDEQ.1998.3497
description: scientific article; zbMATH DE number 1271362