Wolff potential estimates for elliptic equations with nonstandard growth and applications

We study superharmonic functions related to elliptic equations with structural conditions involving a variable growth exponent. We establish pointwise estimates for such functions in terms of a Wolff type potential. We apply these estimates to prove a variable exponent version of the Hedberg–Wolff t...

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Bibliographic Details
Published inForum mathematicum Vol. 22; no. 6; pp. 1061 - 1087
Main Authors Lukkari, Teemu, Maeda, Fumi-Yuki, Marola, Niko
Format Journal Article
LanguageEnglish
Published Berlin Walter de Gruyter GmbH & Co. KG 01.11.2010
Walter de Gruyter GmbH
Subjects
Estimates
Exponents
Mathematical analysis
Sobolev space
Superharmonics
Theorems
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Summary:We study superharmonic functions related to elliptic equations with structural conditions involving a variable growth exponent. We establish pointwise estimates for such functions in terms of a Wolff type potential. We apply these estimates to prove a variable exponent version of the Hedberg–Wolff theorem on the dual of Sobolev spaces with zero boundary values.
Bibliography:ark:/67375/QT4-BSK8S0PL-Z
istex:79F7A48A364D7D4F766B47241EFA21F9854CC3BB
ArticleID:form.22.6.1061
forum.2010.057.pdf
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0933-7741
1435-5337
DOI:10.1515/forum.2010.057