Harnack inequality and continuity of solutions to elliptic equations with nonstandard growth conditions and lower order terms

被引：10

作者：

Liskevich, Vitali ^{[1
]}

Skrypnik, Igor I. ^{[2
]}

机构：

[1] Swansea Univ, Dept Math, Swansea SA2 8PP, W Glam, Wales

[2] Inst Appl Math & Mech, UA-83114 Donetsk, Ukraine

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2010年 / 189卷 / 02期

关键词：

Equations with nonstandard growth conditions; Harnack inequality; Continuity; Nonlinear Kato-class;

D O I：

10.1007/s10231-009-0111-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the Harnack inequality and continuity of solutions for a general class of divergence-type elliptic equations with nonstandard growth measurable coefficients in the main part and lower order terms from nonlinear Kato-type classes.

引用

页码：335 / 356

页数：22

共 50 条

[31] QUASILINEAR ELLIPTIC EQUATIONS WITH NATURAL GROWTH TERMS: THE REGULARIZING EFFECT OF THE LOWER ORDER TERMS
Boccardo, Lucio
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2006, 7 (03) : 355 - 365
[32] HOLDER CONTINUITY UP TO THE BOUNDARY OF SOLUTIONS TO NONLINEAR FOURTH-ORDER ELLIPTIC EQUATIONS WITH NATURAL GROWTH TERMS
Bonafede, Salvatore
Voitovych, Mykhailo V.
DIFFERENTIAL EQUATIONS & APPLICATIONS, 2019, 11 (01): : 107 - 127
[33] Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations
Bella, Peter
Schaeffner, Mathias
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2021, 74 (03) : 453 - 477
[34] Harnack's inequality for solutions to the linearized Monge-Ampere operator with lower-order terms
Maldonado, Diego
JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (06) : 1987 - 2022
[35] HARNACK'S INEQUALITY FOR QUASILINEAR ELLIPTIC EQUATIONS WITH GENERALIZED ORLICZ GROWTH
Shan, Maria A.
Skrypnik, Igor I.
Voitovych, Mykhailo V.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2021,
[36] A Harnack's inequality and Holder continuity for solutions of mixed type evolution equations
Paronetto, Fabio
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI, 2015, 26 (04) : 385 - 395
[37] Quantitative uniqueness of solutions to second-order elliptic equations with singular lower order terms
Davey, Blair
Zhu, Jiuyi
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2019, 44 (11) : 1217 - 1251
[38] Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term
Polidoro, Sergio
Ragusa, Maria Alessandra
REVISTA MATEMATICA IBEROAMERICANA, 2008, 24 (03) : 1011 - 1046
[39] The Harnack inequality in ℝ2 for quasilinear elliptic equations
P. Pucci
J. Serrin
Journal d’Analyse Mathématique, 2001, 85 : 307 - 321
[40] NARROW DOMAINS AND THE HARNACK INEQUALITY FOR ELLIPTIC EQUATIONS
Safonov, M. V.
ST PETERSBURG MATHEMATICAL JOURNAL, 2016, 27 (03) : 509 - 522

← 1 2 3 4 5 →