English

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}
}