Global higher integrability for parabolic quasiminimizers in metric spaces

TL;DR

This paper establishes higher integrability results for parabolic quasiminimizers in metric spaces, extending regularity theory for heat equation-related functions under minimal assumptions.

Contribution

It proves higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces with doubling measure and Poincaré inequality.

Findings

Higher integrability up to the boundary is achieved.

Results apply to metric spaces supporting a weak Poincaré inequality.

The work extends regularity theory for heat equation-related functions.

Abstract

We prove higher integrability up to the boundary for minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces, related to the heat equation. We assume the underlying metric measure space to be equipped with a doubling measure and to support a weak Poincar\'e-inequality.