Gaussian estimates for degenerate diffusion
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- by Michal Chovanec
- Proc. Amer. Math. Soc. 140 (2012), 3947-3957
- DOI: https://doi.org/10.1090/S0002-9939-2012-11313-9
- Published electronically: March 23, 2012
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Abstract:
We prove estimates of Gaussian type for the kernel of the semigroup associated to the operator $m\triangle$, where $m$ is a positive function which may vanish at the boundary (and thus the operator may not be strongly elliptic). No regularity conditions either on the boundary of the domain or on the function $m$ are posed. The optimality of the growth condition on $m$ is discussed.References
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Bibliographic Information
- Michal Chovanec
- Affiliation: Graduiertenkolleg 1100, University of Ulm, 89081 Ulm, Germany
- Address at time of publication: Departement Mathematik, HG J 43, ETH Zürich, Rämisstrasse 101, 8092 Zürich, Switzerland
- Email: michal.chovanec@uni-ulm.de
- Received by editor(s): October 25, 2010
- Received by editor(s) in revised form: May 11, 2011
- Published electronically: March 23, 2012
- Communicated by: Matthew J. Gursky
- © Copyright 2012 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 140 (2012), 3947-3957
- MSC (2010): Primary 35K65, 35K08, 47D06
- DOI: https://doi.org/10.1090/S0002-9939-2012-11313-9
- MathSciNet review: 2944734