Symmetry and compact embeddings for critical exponents in metric-measure spaces

被引：1

作者：

Gaczkowski, Michal ^{[1
]}

Gorka, Przemyslaw ^{[1
]}

Pons, Daniel J. ^{[2
]}

机构：

[1] Warsaw Univ Technol, Dept Math & Informat Sci, Ul Koszykowa 75, PL-00662 Warsaw, Poland

[2] Univ Andres Bello, Fac Ciencias Exactas, Dept Matemat, Republ 498, Santiago, Chile

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2020年 / 269卷 / 11期

关键词：

Sobolev spaces; Metric-measure spaces; Compact embedding; SOBOLEV SPACES;

D O I：

10.1016/j.jde.2020.06.062

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometrics in compact manifolds. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：9819 / 9837

页数：19

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