The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

被引：28

作者：

Benyaiche, Allami ^{[1
]}

Harjulehto, Petteri ^{[2
]}

Hasto, Peter ^{[2
]}

Karppinen, Arttu ^{[2
]}

机构：

[1] Ibn Tofail Univ, Dept Math, Kenitra, Morocco

[2] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 275卷

关键词：

Nonstandard growth; Supersolution; Harnack's inequality; Musielak-Orlicz spaces; Variable exponent; Double phase; NONLINEAR ELLIPTIC-EQUATIONS; DOUBLE-PHASE PROBLEMS; RENORMALIZED SOLUTIONS; HOLDER CONTINUITY; REGULARITY; FUNCTIONALS; MINIMIZERS; SPACES;

D O I：

10.1016/j.jde.2020.11.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak-Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a suitable Lebesgue or Sobolev space. Furthermore, we establish the sharpness of our central assumptions. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：790 / 814

页数：25

共 50 条

[41] LOG-TRANSFORM AND THE WEAK HARNACK INEQUALITY FOR KINETIC FOKKER-PLANCK EQUATIONS
Guerand, Jessica
Imbert, Cyril
JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2023, 22 (06) : 2749 - 2774
[42] Abstract weak Harnack inequality, multiple fixed points and p-Laplace equations
Precup, Radu
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2012, 12 (1-2) : 193 - 206
[43] Weak Harnack's Inequality for non-negative solutions of elliptic equations with potential
Mohammed, A
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (09) : 2617 - 2621
[44] Abstract weak Harnack inequality, multiple fixed points and p-Laplace equations
Radu Precup
Journal of Fixed Point Theory and Applications, 2012, 12 : 193 - 206
[45] Weak Harnack inequality for doubly non-linear equations of slow diffusion type
Baeuerlein, Fabian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 539 (02)
[46] HARNACK INEQUALITY FOR DEGENERATE PARABOLIC EQUATIONS
GUTIERREZ, CE
WHEEDEN, RL
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1991, 16 (4-5) : 745 - 770
[47] A HARNACK INEQUALITY FOR DEGENERATE PARABOLIC EQUATIONS
CHIARENZA, FM
SERAPIONI, RP
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1984, 9 (08) : 719 - 749
[48] A Harnack inequality for ordinary differential equations
Berhanu, S
Mohammed, A
AMERICAN MATHEMATICAL MONTHLY, 2005, 112 (01): : 32 - 41
[49] DEGENERATE PARABOLIC EQUATIONS AND HARNACK INEQUALITY
CHIARENZA, F
SERAPIONI, R
ANNALI DI MATEMATICA PURA ED APPLICATA, 1984, 137 : 139 - 162
[50] HARNACK INEQUALITY FOR PARABOLIC DIFFERENTIAL EQUATIONS
MOSER, J
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1964, 17 (01) : 101 - &

← 1 2 3 4 5 →