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

TL;DR

This paper establishes a local Calderón-Zygmund estimate for the singular parabolic double-phase system, extending previous results to the case where p<2 using phase analysis and intrinsic geometry techniques.

Contribution

It provides the first Calderón-Zygmund estimate for the p<2 case of the singular parabolic double-phase system, employing phase analysis and intrinsic geometry methods.

Findings

Established Calderón-Zygmund estimate for p<2 case

Introduced phase analysis for intrinsic geometry

Utilized comparison estimates and scaling invariance

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.