Parabolic comparison principle and quasiminimizers in metric measure spaces

Kinnunen, Juha; Masson, Mathias

doi:10.1090/S0002-9939-2014-12236-2

Parabolic comparison principle and quasiminimizers in metric measure spaces
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by Juha Kinnunen and Mathias Masson PDF

Proc. Amer. Math. Soc. 143 (2015), 621-632 Request permission

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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