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

Michał Gaczkowski, Przemysław Górka, Daniel J. Pons

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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 isometries in compact manifolds.

Original languageEnglish
Pages (from-to)9819-9837
Number of pages19
JournalJournal of Differential Equations
Volume269
Issue number11
DOIs
Publication statusPublished - 15 Nov 2020

Keywords

  • Compact embedding
  • Metric-measure spaces
  • Sobolev spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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