Global maximal regularity for equations with degenerate weights

In this paper we are concerned with global maximal regularity estimates for elliptic equations with degenerate weights. We consider both the linear case and the non-linear case. We show that higher integrability of the gradients can be obtained by imposing a local small oscillation condition on the...

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Bibliographic Details
Published inJournal de mathématiques pures et appliquées Vol. 177; pp. 484 - 530
Main Authors Balci, Anna Kh, Byun, Sun-Sig, Diening, Lars, Lee, Ho-Sik
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.09.2023
Subjects
Degenerate weight
Lipschitz boundary
p-Laplacian
Regularity of solutions
Degenerate weight
p-Laplacian
Lipschitz boundary
35J70
Regularity of solutions
35B65
35J25
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Summary:In this paper we are concerned with global maximal regularity estimates for elliptic equations with degenerate weights. We consider both the linear case and the non-linear case. We show that higher integrability of the gradients can be obtained by imposing a local small oscillation condition on the weight and a local small Lipschitz condition on the boundary of the domain. Our results are new in the linear and non-linear case. We show by example that the relation between the exponent of higher integrability and the smallness parameters is sharp even in the linear or the unweighted case.
ISSN:0021-7824
DOI:10.1016/j.matpur.2023.07.010