Interior regularity results for inhomogeneous anisotropic quasilinear equations

被引：11

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

[11] LOCAL REGULARITY PROPERTIES FOR THE SOLUTIONS OF A NON-LINEAR PARTIAL-DIFFERENTIAL EQUATION
DETHELIN, F
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (08) : 839 - 844
[12] C1+ALPHA LOCAL REGULARITY OF WEAK SOLUTIONS OF DEGENERATE ELLIPTIC-EQUATIONS
DIBENEDETTO, E
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1983, 7 (08) : 827 - 850
[13] Giaquinta M., 2012, INTRO REGULARITY THE
[14] GIUSTI E., 2005, DIRECT METHODS CALCU
[15] Guarnotta U., 2021, ARXIV
[16] Leoni G., 1 COURSE SOBOLEV SPA
[17] SHARP FORMS OF ESTIMATES FOR SUBSOLUTIONS AND SUPERSOLUTIONS OF QUASI-LINEAR ELLIPTIC-EQUATIONS INVOLVING MEASURES
LIEBERMAN, GM
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (7-8) : 1191 - 1212
[18] THE NATURAL GENERALIZATION OF THE NATURAL CONDITIONS OF LADYZHENSKAYA AND URALTSEVA FOR ELLIPTIC-EQUATIONS
LIEBERMAN, GM
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (2-3) : 311 - 361
[19] On singular sets of local solutions to p-Laplace equations
Lou, Hongwei
[J]. CHINESE ANNALS OF MATHEMATICS SERIES B, 2008, 29 (05) : 521 - 530
[20] MARCUS M, 1972, ARCH RATION MECH AN, V45, P294

← 1 2 3 →