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Heat kernel estimates for an operator with a singular drift and isoperimetric inequalities

  • Alexander Grigor’yan EMAIL logo , Shunxiang Ouyang and Michael Röckner
Published/Copyright: July 7, 2015

Abstract

In the present paper we prove upper and lower bounds of the heat kernel for the operator Δ-(|x|-α) in n{0}, where α>0. We obtain these bounds from an isoperimetric inequality for a measure e-|x|-αdx on n{0}. The latter amounts to a certain functional isoperimetric inequality for the radial part of this measure.

Funding statement: Supported by SFB 701 of the German Research Council.

Acknowledgements

We would like to thank Yuri Kondratiev for stimulating discussions that motivated this work, and the anonymous referee for his/her careful reading and useful suggestions, leading to some improvement and simplification.

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Received: 2012-12-6
Revised: 2015-3-1
Published Online: 2015-7-7
Published in Print: 2018-3-1

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