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arXiv · 1301.3765

On the Harnack inequality for parabolic minimizers in metric measure spaces

Niko Marola·Mathias Masson
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Abstract

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.

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Niko Marola, Mathias Masson. 2013-04-16. On the Harnack inequality for parabolic minimizers in metric measure spaces. https://doi.org/10.2748/tmj%2F1386354296

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