Regularity results for quasiminima of a class of double phase problems

TL;DR

This paper establishes regularity properties such as boundedness, H"older continuity, and Harnack inequalities for quasiminima of double phase elliptic problems in metric measure spaces, using variational and De Giorgi methods.

Contribution

It extends regularity results for double phase problems to the setting of metric measure spaces, employing a variational approach and intrinsic geometric estimates.

Findings

Proved boundedness of quasiminima

Established H"older continuity

Derived Harnack inequalities

Abstract

We prove boundedness, H\"older continuity, Harnack inequality results for local quasiminima to elliptic double phase problems of $p$-Laplace type in the general context of metric measure spaces. The proofs follow a variational approach and they are based on the De Giorgi method, a careful phase analysis and estimates in the intrinsic geometries.