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arXiv · 1301.3774

Parabolic comparison principle and quasiminimizers in metric measure spaces

Juha Kinnunen·Mathias Masson
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Abstract

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.

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Juha Kinnunen, Mathias Masson. 2013-01-16. Parabolic comparison principle and quasiminimizers in metric measure spaces. https://arxiv.org/abs/1301.3774

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