Wolff potential estimates for supersolutions of equations with generalized Orlicz growth

TL;DR

This paper derives pointwise Wolff potential estimates for supersolutions of quasilinear elliptic equations with generalized Orlicz growth, leading to Harnack inequalities and local Hölder continuity results.

Contribution

It introduces new Wolff potential estimates for equations with generalized Orlicz growth, extending regularity theory for such nonlinear PDEs.

Findings

Supersolutions satisfy pointwise Wolff potential estimates.

Supersolutions obey Harnack inequality under certain conditions.

Supersolutions are locally Hölder continuous.

Abstract

In this paper, we establish pointwise estimates for supersolutions of quasilinear elliptic equations with structural conditions involving a generalized Orlicz growth in terms of a Wolff type potential. As a consequence, under the extra assumption, we obtain that the supersolutions satisfy a Harnack inequality and local H\"older continuity.