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 49 条

[1]

Alkhutov YA, 1997, DIFF EQUAT+, V33, P1653

[2] A Harnack inequality in Orlicz-Sobolev spaces [J].