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 Poincaré inequality is supported. We give proofs to density results concerning the space of test functions used when proving estimates for parabolic quasiminimizers.

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