Variable exponent Sobolev spaces and regularity of domains-II

Przemysław Górka, Nijjwal Karak, Daniel J. Pons

Research output: Contribution to journalArticlepeer-review

Abstract

We provide necessary conditions on Euclidean domains for inclusions W1,p(·)(Ω) ↪ Lq(·)(Ω) of variable exponent Sobolev spaces. The conditions on the exponent p(·) are log-Hölder and log-log-Hölder continuity, while those on the domain Ω are the measure and the log measure density conditions. Restrictions on the exponents q(·) and p(·) appearing in Górka et al. (J. Geom. Anal. 310: 7304-7319, 2021) are relaxed, improving the results obtained in that work.

Original languageEnglish
JournalRevista Matematica Complutense
DOIs
Publication statusAccepted/In press - 2023

Keywords

  • Measure density condition
  • Sobolev embedding
  • Sobolev spaces

ASJC Scopus subject areas

  • General Mathematics

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