Calderón–Zygmund estimates for generalized double phase equations with matrix weights

Abstract

Abstract We prove Calderón–Zygmund estimates for generalized double phase equations with Orlicz growth and variable matrix weights. The operator combines a nonuniformly elliptic double phase structure with a degenerate or singular matrix weight satisfying a small log‐ 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 Calderón–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 previous results.