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

[21] Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients
Koike, Shigeaki
Swiech, Andrzej
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2009, 61 (03) : 723 - 755
[22] Harnack inequality for the nonlocal equations with general growth
Fang, Yuzhou
Zhang, Chao
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2023, 153 (05) : 1479 - 1502
[23] HARNACK INEQUALITY FOR WEAK SOLUTIONS OF DEGENERATE QUASILINEAR ELLIPTIC EQUATIONS
EDMUNDS, DE
PELETIER, LA
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1972, 5 (JUN): : 21 - &
[24] A weak Harnack inequality for fractional evolution equations with discontinuous coefficients
Zacher, Rico
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2013, 12 (04) : 903 - 940
[25] A Harnack inequality in Orlicz-Sobolev spaces
Arriagad, Waldo
Huentutripay, Jorge
STUDIA MATHEMATICA, 2018, 243 (02) : 117 - 137
[26] A remark on the weak Harnack inequality
Maldonado, Diego
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 549 (01)
[27] Harnack inequality and applications for stochastic generalized porous media equations
Wang, Feng-Yu
ANNALS OF PROBABILITY, 2007, 35 (04): : 1333 - 1350
[28] On the weak Harnack inequality for unbounded non-negative super-solutions of degenerate double-phase parabolic equations
Savchenko, Mariia
Skrypnik, Igor
Yevgenieva, Yevgeniia
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 537 (02)
[29] Harnack inequality and continuity of weak solutions for doubly degenerate elliptic equations
Di Fazio, G.
Fanciullo, M. S.
Zamboni, P.
MATHEMATISCHE ZEITSCHRIFT, 2019, 292 (3-4) : 1325 - 1336
[30] ON THE WEAK HARNACK INEQUALITY FOR QUASI-LINEAR ELLIPTIC-EQUATIONS
DAVYDOVA, LV
MATHEMATICS OF THE USSR-SBORNIK, 1984, 125 (3-4): : 335 - 349

← 1 2 3 4 5 →