A note on heat kernel estimates, resistance bounds and Poincar\'e inequality
Probability
2018-10-24 v2 Analysis of PDEs
Abstract
Sub-Gaussian heat kernel estimates are typical of fractal graphs. We show that sub-Gaussian estimates on graphs follow from a Poincar\'e inequality, capacity upper bound, and a slow volume growth condition. An important feature of this work is that we do not assume elliptic Harnack inequality, cutoff Sobolev inequality, or exit time bounds.
Keywords
Cite
@article{arxiv.1809.00767,
title = {A note on heat kernel estimates, resistance bounds and Poincar\'e inequality},
author = {Mathav Murugan},
journal= {arXiv preprint arXiv:1809.00767},
year = {2018}
}
Comments
17 pages. arXiv admin note: text overlap with arXiv:1803.11296; fixed some typos and added a few references