Variable Exponent Sobolev Spaces and Regularity of Domains

Przemysław Górka; Nijjwal Karak; Daniel J. Pons

doi:10.1007/s12220-020-00499-8

Variable Exponent Sobolev Spaces and Regularity of Domains

Przemysław Górka, Nijjwal Karak, Daniel J. Pons

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

5 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	7304-7319
Número de páginas	16
Publicación	Journal of Geometric Analysis
Volumen	31
N.º	7
DOI	https://doi.org/10.1007/s12220-020-00499-8
Estado	En prensa - 2020

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Geometría y topología

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10.1007/s12220-020-00499-8

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title = "Variable Exponent Sobolev Spaces and Regularity of Domains",

abstract = "We study the embeddings of variable exponent Sobolev and H{\"o}lder 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-H{\"o}lder continuity; concerning the domain, the relevant condition is the measure density condition.",

keywords = "Measure density condition, Sobolev embedding, Sobolev spaces",

author = "Przemys{\l}aw G{\'o}rka and Nijjwal Karak and Pons, {Daniel J.}",

note = "Funding Information: N. K. thanks DST-SERB (Project PDF/2016/000328) for financial support. P. G. has been supported by NCN grant 2018/02/X/ST1/02133. All the Authors would like to thank the reviewer for his/her valuable comments on the manuscript. Publisher Copyright: {\textcopyright} 2020, The Author(s).",

year = "2020",

doi = "10.1007/s12220-020-00499-8",

language = "English",

volume = "31",

pages = "7304--7319",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer New York",

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TY - JOUR

T1 - Variable Exponent Sobolev Spaces and Regularity of Domains

AU - Górka, Przemysław

AU - Karak, Nijjwal

AU - Pons, Daniel J.

N1 - Funding Information: N. K. thanks DST-SERB (Project PDF/2016/000328) for financial support. P. G. has been supported by NCN grant 2018/02/X/ST1/02133. All the Authors would like to thank the reviewer for his/her valuable comments on the manuscript. Publisher Copyright: © 2020, The Author(s).

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Measure density condition

KW - Sobolev embedding

KW - Sobolev spaces

UR - http://www.scopus.com/inward/record.url?scp=85089731978&partnerID=8YFLogxK

U2 - 10.1007/s12220-020-00499-8

DO - 10.1007/s12220-020-00499-8

M3 - Article

AN - SCOPUS:85089731978

SN - 1050-6926

VL - 31

SP - 7304

EP - 7319

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

IS - 7

ER -

Variable Exponent Sobolev Spaces and Regularity of Domains

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