Davies’ method for anomalous diffusions
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- by Mathav Murugan and Laurent Saloff-Coste PDF
- Proc. Amer. Math. Soc. 145 (2017), 1793-1804 Request permission
Abstract:
Davies’ method of perturbed semigroups is a classical technique to obtain off-diagonal upper bounds on the heat kernel. However Davies’ method does not apply to anomalous diffusions due to the singularity of energy measures. In this note, we overcome the difficulty by modifying the Davies’ perturbation method to obtain sub-Gaussian upper bounds on the heat kernel. Our computations closely follow the seminal work of Carlen, Kusuoka and Stroock (1987). However, a cutoff Sobolev inequality due to Andres and Barlow (2015) is used to bound the energy measure.References
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Additional Information
- Mathav Murugan
- Affiliation: Department of Mathematics, University of British Columbia and Pacific Institute for the Mathematical Sciences, Vancouver, British Columbia V6T 1Z2, Canada
- MR Author ID: 864378
- Email: mathav@math.ubc.ca
- Laurent Saloff-Coste
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 153585
- Email: lsc@math.cornell.edu
- Received by editor(s): February 3, 2016
- Received by editor(s) in revised form: May 26, 2016, and June 6, 2016
- Published electronically: October 18, 2016
- Additional Notes: Both authors were partially supported by NSF grant DMS 1404435
- Communicated by: Mark M. Meerschaert
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1793-1804
- MSC (2010): Primary 60J60, 60J35
- DOI: https://doi.org/10.1090/proc/13324
- MathSciNet review: 3601569