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Gaussian estimates for degenerate diffusion


Author: Michal Chovanec
Journal: Proc. Amer. Math. Soc. 140 (2012), 3947-3957
MSC (2010): Primary 35K65, 35K08, 47D06
Published electronically: March 23, 2012
MathSciNet review: 2944734
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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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11313-9
Keywords: Heat equation, degenerate diffusion, kernel estimates, semigroups
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
Article copyright: © Copyright 2012 American Mathematical Society