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2013 On the Harnack inequality for parabolic minimizers in metric measure spaces
Niko Marola, Mathias Masson
Tohoku Math. J. (2) 65(4): 569-589 (2013). DOI: 10.2748/tmj/1386354296

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 Grigoryan--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. "On the Harnack inequality for parabolic minimizers in metric measure spaces." Tohoku Math. J. (2) 65 (4) 569 - 589, 2013. https://doi.org/10.2748/tmj/1386354296

Information

Published: 2013
First available in Project Euclid: 6 December 2013

zbMATH: 1293.30096
MathSciNet: MR3161434
Digital Object Identifier: 10.2748/tmj/1386354296

Subjects:
Primary: 35B65
Secondary: 35K55 , 49N60

Keywords: doubling measure , Harnack inequality , metric space , minimizer , Newtonian space , parabolic‎ , Poincaré inequality

Rights: Copyright © 2013 Tohoku University

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Vol.65 • No. 4 • 2013
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