Calder\'on-Zygmund type estimate for the singular parabolic double-phase system

Abstract

This paper discusses the local Calder\'on-Zygmund type estimate for the singular parabolic double-phase system. The proof covers the counterpart $p<2$ of the result in [23]. Phase analysis is employed to determine an appropriate intrinsic geometry for each phase. Comparison estimates and scaling invariant properties for each intrinsic geometry are the main techniques to obtain the main estimate.