Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth

TL;DR

This paper establishes Harnack's inequality for solutions to quasilinear elliptic equations with generalized Orlicz growth, extending the inequality to new variable exponent and (p,q) growth scenarios.

Contribution

It introduces a novel proof of Harnack's inequality applicable to a broader class of elliptic equations with generalized Orlicz growth conditions.

Findings

Harnack's inequality holds for solutions with generalized Orlicz growth.

The approach covers variable exponent and (p,q) growth cases.

The results extend classical inequalities to more complex growth conditions.

Abstract

We prove Harnack's inequality for bounded weak solutions to quasilinear second order elliptic equations with generalized Orlicz growth conditions. Our approach covers new cases of variable exponent and (p,q) growth conditions.