Variable Exponent Sobolev Spaces and Regularity of Domains

Górka, P.Karak, N.Pons, D.2021-10-192021-10-192020Journal of Geometric Analysis, Volume 31, Issue 7, Pages 7304 - 7319, July 20211050-6926http://repositorio.unab.cl/xmlui/handle/ria/20544Indexación: 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.enMeasure density conditionSobolev embeddingSobolev spacesVariable Exponent Sobolev Spaces and Regularity of DomainsArtículoAttribution 4.0 International (CC BY 4.0)DOI: 10.1007/s12220-020-00499-8