Harnack's Inequality for Parabolic De Giorgi Classes in Metric Spaces
Analysis of PDEs
2013-08-14 v2
Abstract
In this paper we study problems related to parabolic partial differential equations in metric measure spaces equipped with a doubling measure and supporting a Poincare' inequality. We give a definition of parabolic De Giorgi classes and compare this notion with that of parabolic quasiminimizers. The main result, after proving the local boundedness, is a scale and location invariant Harnack inequality for functions belonging to parabolic De Giorgi classes. In particular, the results hold true for parabolic quasiminimizers.
Keywords
Cite
@article{arxiv.1106.5356,
title = {Harnack's Inequality for Parabolic De Giorgi Classes in Metric Spaces},
author = {J. Kinnunen and N. Marola and M. Miranda and F. Paronetto},
journal= {arXiv preprint arXiv:1106.5356},
year = {2013}
}