# Global higher integrability of weak solutions of porous medium systems

## TL;DR

This paper proves that the gradient of weak solutions to porous medium systems has higher integrability properties up to the boundary, extending the understanding of regularity for these nonlinear PDEs.

## Contribution

It establishes the higher integrability of the gradient of weak solutions to porous medium systems up to the boundary, including initial and lateral boundaries.

## Key findings

- Gradient of solutions is integrable to a higher power than the natural power 2.
- Results include boundary and initial boundary cases.
- Provides new regularity results for porous medium type systems.

## Abstract

We establish higher integrability up to the boundary for the gradient of solutions to porous medium type systems, whose model case is given by \begin{equation*} \partial_t u-\Delta(|u|^{m-1}u)=\mathrm{div}\,F\,, \end{equation*} where $m>1$. More precisely, we prove that under suitable assumptions the spatial gradient $D(|u|^{m-1}u)$ of any weak solution is integrable to a larger power than the natural power $2$. Our analysis includes both the case of the lateral boundary and the initial boundary.