Variable Exponent Sobolev Spaces and Regularity of Domains

Przemysław Górka, Nijjwal Karak, Daniel J. Pons

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We study the embeddings of variable exponent Sobolev and Hölder function spaces over Euclidean domains, providing necessary and/or sufficient conditions on the regularity of the exponent and/or the domain in various contexts. Concerning the exponent, the relevant condition is log-Hölder continuity; concerning the domain, the relevant condition is the measure density condition.

Original languageEnglish
Pages (from-to)7304-7319
Number of pages16
JournalJournal of Geometric Analysis
Issue number7
Publication statusAccepted/In press - 2020


  • Measure density condition
  • Sobolev embedding
  • Sobolev spaces

ASJC Scopus subject areas

  • Geometry and Topology


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