Local higher integrability for parabolic quasiminimizers in metric spaces

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.