Parabolic comparison principle and quasiminimizers in metric measure spaces
Analysis of PDEs
2013-01-17 v1
Abstract
We give several characterizations of parabolic (quasisuper)- minimizers in a metric measure space equipped with a doubling measure and supporting a Poincar\'e 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.
Keywords
Cite
@article{arxiv.1301.3774,
title = {Parabolic comparison principle and quasiminimizers in metric measure spaces},
author = {Juha Kinnunen and Mathias Masson},
journal= {arXiv preprint arXiv:1301.3774},
year = {2013}
}