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

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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2021-02, Vol.275, p.790-814
Main Authors: Benyaiche, Allami, Harjulehto, Petteri, Hästö, Peter, Karppinen, Arttu
Format: Article
Language:English
Subjects:
Double phase
Harnack's inequality
Musielak–Orlicz spaces
Nonstandard growth
Supersolution
Variable exponent
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.11.007