Matrix weights and regularity for degenerate elliptic equations

被引：3

作者：

Di Fazio, Giuseppe ^{[1
]}

Fanciullo, Maria Stella ^{[1
]}

Monticelli, Dario Daniele ^{[2
]}

Rodney, Scott ^{[3
]}

Zamboni, Pietro ^{[1
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, Catania, Italy

[2] Politecn Milano F Brioschi, Dept Math, Milan, Italy

[3] Cape Breton Univ, Dept Math Phys & Geol, Sydney, NS B1P 6L2, Canada

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2023年 / 237卷

关键词：

Degenerate elliptic operators; Stummel class; Harnack inequality; Weights; QUASI-LINEAR EQUATIONS; COMPACT EMBEDDING THEOREM; HARNACK INEQUALITY; WEAK SOLUTIONS; POINCARE INEQUALITIES; LOCAL BEHAVIOR; CONTINUITY;

D O I：

10.1016/j.na.2023.113363

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove local boundedness, Harnack inequality and local regularity for weak solutions of quasilinear degenerate elliptic equations in divergence form. Degeneracy is via a non negative, symmetric, measurable matrix-valued function Q(x) and two suitable non negative weight functions. We setup an axiomatic approach in terms of suitable geometric conditions and local Sobolev-Poincare inequalities. Data integrability is close to L1 and it is exploited in terms of suitable version of Stummel-Kato class that in some cases is also necessary to the regularity.(c) 2023 Elsevier Ltd. All rights reserved.

引用

页数：24

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