Sobolev spaces in the presence of symmetries
type: Item
instance of: scholarly article
title: Sobolev spaces in the presence of symmetries
zbMATH Open document ID: 0886.58003
DOI: 10.1016/S0021-7824(97)89975-8
author: Emmanuel Hebey
author: Michel Vaugon
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 1997-09-15T00:00:00Z
review text: We prove that Sobolev embeddings can be improved in the presence of symmetries. This includes embeddings in higher \(L^p\)-spaces and compactness properties of these embeddings. While such phenomena have been observed in specific context by several authors, we treat here the case of arbitrary Riemannian manifolds (where, in particular, no global chart exist). On the one hand, it turns out that when dealing with compact manifolds, one just has to consider the minimum orbit dimension of the group acting on the manifold. On the other hand, and when dealing with non compact manifolds, one also has to consider the action of the group at infinity. Complete answers are given.
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1060800
zbMATH Keywords: Sobolev embeddings
zbMATH Keywords: symmetries
zbMATH Keywords: embeddings in higher \(L^ p\)-spaces
zbMATH Keywords: compactness
zbMATH Keywords: Riemannian manifolds
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1060800