Global higher integrability for parabolic quasiminimizers in metric measure spaces

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 Poincaré inequality. The boundary of the domain is assumed to satisfy a regularity condition.