Global maximal regularity for equations with degenerate weights

被引：8

作者：

Balci, Anna Kh. ^{[1
]}

Byun, Sun-Sig ^{[2
]}

Diening, Lars ^{[1
]}

Lee, Ho-Sik ^{[1
]}

机构：

[1] Univ Bielefeld, Fak Math, Univ Str 25, D-33615 Bielefeld, Germany

[2] Seoul Natl Univ, Inst Math, Dept Math Sci & Res, Gwanak Ro 1, Seoul, South Korea

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2023年 / 177卷

基金：

新加坡国家研究基金会;

关键词：

Degenerate weight; Lipschitz boundary; p-Laplacian; Regularity of solutions; OBLIQUE DERIVATIVE PROBLEMS; NONLINEAR ELLIPTIC-EQUATIONS; BOUNDARY-VALUE-PROBLEMS; BMO COEFFICIENTS; LIPSCHITZ-DOMAINS; WEAK SOLUTIONS; GRADIENT; SYSTEMS; INTEGRABILITY; PDES;

D O I：

10.1016/j.matpur.2023.07.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. & COPY; 2023 Elsevier Masson SAS. All rights reserved.

引用

页码：484 / 530

页数：47

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