Interior regularity results for inhomogeneous anisotropic quasilinear equations

被引：16

作者：

Antonini, Carlo Alberto ^{[1
]}

Ciraolo, Giulio ^{[1
]}

Farina, Alberto ^{[2
]}

机构：

[1] Univ Milan, Dipartimento Matemat Federigo Enriques, Via Cesare Saldini 50, I-20133 Milan, Italy

[2] Univ Picardie Jules Verne, LAMFA, CNRS, UMR 7352, 33 Rue St Leu, F-80039 Amiens, France

来源：

MATHEMATISCHE ANNALEN | 2023年 / 387卷 / 3-4期

关键词：

LOCAL REGULARITY; MONOTONICITY; DEGENERATE;

D O I：

10.1007/s00208-022-02500-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider inhomogeneous p-Laplace type equations of the form -div (a del u)) = f in a possibly anisotropic setting. Under general assumptions on the source term f, we obtain quantitative Sobolev regularity results for the stress field a(del u) and weighted L-2 estimates for the Hessian of the solution. As far as we know, our results are new or refine the ones available in literature also when restricted to the Euclidean setting.

引用

页码：1745 / 1776

页数：32

共 26 条

[1]

[Anonymous], 1963, Seminaire Jean Leray

[2]

[Anonymous], 1964, Ann. Scuola Norm. Sup. Pisa Cl. Sci.

[3]

[Anonymous], 1978, Journes dAnalyse Non Linaire, DOI DOI 10.1007/BFB0061807

[4]

[Anonymous], 1963, Annali della Scuola Normale Superiore di Pisa-Scienze Fisiche e Matematiche