Energy inequalities for cutoff functions and some applications
Probability
2015-03-17 v2
Abstract
We consider a metric measure space with a local regular Dirichlet form. We establish necessary and sufficient conditions for upper heat kernel bounds with sub-diffusive space-time exponent to hold. This characterization is stable under rough isometries, that is it is preserved under bounded perturbations of the Dirichlet form. Further, we give a criterion for stochastic completeness in terms of a Sobolev inequality for cutoff functions. As an example we show that this criterion applies to an anomalous diffusion on a geodesically incomplete fractal space, where the well-established criterion in terms of volume growth fails.
Cite
@article{arxiv.1202.0722,
title = {Energy inequalities for cutoff functions and some applications},
author = {Sebastian Andres and Martin T. Barlow},
journal= {arXiv preprint arXiv:1202.0722},
year = {2015}
}