Gradient estimates for parabolic problems with Orlicz growth and discontinuous coefficients

TL;DR

This paper establishes Calderón-Zygmund estimates for parabolic equations with Orlicz growth and discontinuous coefficients, extending regularity theory to more general nonlinear and discontinuous settings.

Contribution

It provides new Calderón-Zygmund type estimates for parabolic problems with Orlicz growth and discontinuous coefficients, including systems with Uhlenbeck structure.

Findings

Calderón-Zygmund estimates derived for equations with Orlicz growth

Extension of regularity results to discontinuous coefficients

Application to parabolic systems with Uhlenbeck structure

Abstract

We obtain Calder\'on-Zygmund type estimates for parabolic equations with Orlicz growth, where nonlinearities involved in the equations may be discontinuous for the space and time variables. In addition, we consider parabolic systems with the Uhlenbeck structure.