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Regularity theory of Kolmogorov operator revisited

Part of: Stochastic analysis Special classes of linear operators Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  24 August 2020

Damir Kinzebulatov
Damir Kinzebulatov*
Affiliation:
Département de mathématiques et de statistique, Université Laval, 1045 av. de la Médecine, Québec, QC G1V 0A6, Canada
*
e-mail:damir.kinzebulatov@mat.ulaval.ca
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Abstract

We consider Kolmorogov operator $-\Delta +b \cdot \nabla $ with drift b in the class of form-bounded vector fields (containing vector fields having critical-order singularities). We characterize quantitative dependence of the Sobolev and Hölder regularity of solutions to the corresponding elliptic equation on the value of the form-bound of b.

Keywords

Elliptic operatorsform-bounded vector fieldsregularity of solutionsFeller semigroups

MSC classification

Primary: 47B44: Accretive operators, dissipative operators, etc.
Secondary: 47D07: Markov semigroups and applications to diffusion processes 60H10: Stochastic ordinary differential equations
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 725 - 736
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

The research of the author is supported by grants from NSERC and FRQNT.

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