Local higher integrability for parabolic quasiminimizers in metric spaces

TL;DR

This paper establishes local higher integrability results for parabolic quasiminimizers' gradients in metric measure spaces, expanding the understanding of their regularity under minimal assumptions.

Contribution

It introduces new density results for test functions and extends higher integrability theory to parabolic quasiminimizers in metric spaces.

Findings

Proved local higher integrability of minimal p-weak upper gradients.

Established density results for test functions in the analysis.

Extended regularity results to metric measure spaces with doubling measures.

Abstract

Using variational methods, we prove local higher integrability for the minimal p-weak upper gradients of parabolic quasiminimizers in metric measure spaces. We assume the measure to be doubling and the underlying space to be such that a weak Poincar\'e inequality is supported. We give proofs to density results concerning the space of test functions used when proving estimates for parabolic quasiminimizers.