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Mathias Masson

Publications and source records attributed to Mathias Masson.

5 recordsLinked to original sources
arXiv2013

On the Harnack inequality for parabolic minimizers in metric measure spaces

In this note we consider problems related to parabolic partial differential equations in geodesic metric measure spaces, that are equipped with a doubling measure and a Poincaré inequality. We prove a location and scale invariant Harnack inequality for a minimizer of a variational problem related to a doubly non-linear parabolic equation involving the p-Laplacian. Moreover, we prove the sufficiency of the Grigor'yan--Saloff-Coste theorem for general p > 1 in geodesic metric spaces. The approach used is strictly variational, and hence we are able to carry out the argument in the metric setting.

math.AP↗
arXiv2013

Global higher integrability for parabolic quasiminimizers in metric 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.

math.AP↗
arXiv2013

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.

math.AP↗
arXiv2013

Parabolic comparison principle and quasiminimizers in metric measure spaces

We give several characterizations of parabolic (quasisuper)- minimizers in a metric measure space equipped with a doubling measure and supporting a Poincaré inequality. We also prove a version of comparison principle for super- and subminimizers on parabolic space-time cylinders and a uniqueness result for minimizers of a boundary value problem. We also give an example showing that the corresponding results do not hold, in general, for quasiminimizers even in the Euclidean case.

math.AP↗