Calderon-Zygmund estimates for generalized double phase equations with matrix weights

TL;DR

This paper establishes Calderon-Zygmund estimates for complex double phase equations with Orlicz growth and matrix weights, advancing the understanding of weighted elliptic PDEs with non-uniform structures.

Contribution

It extends Calderon-Zygmund theory to generalized double phase equations with matrix weights and Orlicz growth, unifying previous results in a broader framework.

Findings

Higher integrability of weighted data implies higher integrability of the weighted gradient.

The results unify and extend existing Calderon-Zygmund estimates for double phase and weighted elliptic equations.

The operator handles non-uniform ellipticity and degenerate or singular matrix weights under small log-BMO conditions.

Abstract

We prove Calderon-Zygmund estimates for generalized double phase equations with Orlicz growth and variable matrix weights. The operator combines a non-uniformly elliptic double phase structure with a degenerate or singular matrix weight satisfying a small log-BMO condition. Under appropriate structural assumptions, we show that higher integrability of the weighted datum yields higher integrability of the weighted gradient of weak solutions. Our results extend the existing Calderon-Zygmund theory for double phase problems and weighted elliptic equations to a unified framework capturing the interaction between Orlicz growth and matrix-weighted structures, thereby building upon and unifying the results in [BBO20] and [BCR26].