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

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].