Variable exponent Sobolev spaces and regularity of domains-II

Przemysław Górka; Nijjwal Karak; Daniel J. Pons

doi:10.1007/s13163-023-00470-5

Variable exponent Sobolev spaces and regularity of domains-II

Przemysław Górka, Nijjwal Karak, Daniel J. Pons

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

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Resumen

We provide necessary conditions on Euclidean domains for inclusions W¹^,^p⁽^·⁾(Ω) ↪ L^q⁽^·⁾(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.

Idioma original	Inglés
Publicación	Revista Matematica Complutense
DOI	https://doi.org/10.1007/s13163-023-00470-5
Estado	En prensa - 2023

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title = "Variable exponent Sobolev spaces and regularity of domains-II",

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-H{\"o}lder and log-log-H{\"o}lder 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 G{\'o}rka et al. (J. Geom. Anal. 310: 7304-7319, 2021) are relaxed, improving the results obtained in that work.",

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

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

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year = "2023",

doi = "10.1007/s13163-023-00470-5",

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T1 - Variable exponent Sobolev spaces and regularity of domains-II

AU - Górka, Przemysław

AU - Karak, Nijjwal

AU - Pons, Daniel J.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Measure density condition

KW - Sobolev embedding

KW - Sobolev spaces

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DO - 10.1007/s13163-023-00470-5

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JO - Revista Matematica Complutense

JF - Revista Matematica Complutense

ER -

Variable exponent Sobolev spaces and regularity of domains-II

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