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arXiv · 1202.0722

Energy inequalities for cutoff functions and some applications

Sebastian Andres·Martin T. Barlow
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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.

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Sebastian Andres, Martin T. Barlow. 2013-01-09. Energy inequalities for cutoff functions and some applications. https://doi.org/10.1515/crelle-2013-0009

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