Local boundedness and higher integrability for the sub-critical singular porous medium system

TL;DR

This paper proves that the gradient of weak solutions to sub-critical singular porous medium systems has higher integrability than initially assumed, advancing understanding of these equations.

Contribution

It establishes higher integrability results for the gradient in the critical and sub-critical singular porous medium systems, completing the theoretical framework.

Findings

Gradient of solutions has higher integrability

Results apply to critical and sub-critical singular cases

Completes the theoretical understanding of porous medium systems

Abstract

The gradient of weak solutions to porous medium-type equations or systems possesses a higher integrability than the one assumed in the pure notion of a solution. We settle the critical and sub-critical, singular case and complete the program.