Double phase meets Muckenhoupt
Analysis of PDEs
2026-01-29 v1 Functional Analysis
Abstract
In this paper we generalize the famous result of [FKS] to the double phase model. In particular, we work with minimal assumptions on the modulating coefficient by introducing a Muckenhoupt-type condition on generalized Orlicz spaces. We develop a complete theory equivalent to that of classical Muckenhoupt weights, including the boundedness of the maximal operator and Sobolev-Poincare estimates. We combine this with the De~Giorgi technique to show H\"older continuity of the solutions.
Keywords
Cite
@article{arxiv.2601.20736,
title = {Double phase meets Muckenhoupt},
author = {Daviti Adamadze and Lars Diening and Tengiz Kopaliani and Jihoon Ok},
journal= {arXiv preprint arXiv:2601.20736},
year = {2026}
}