Applications of Zvonkin’s Transform to Stationary Kolmogorov Equations

— In this note we develop a new analytic version of Zvonkin’s transform of the drift coefficient of a stationary Kolmogorov equation and apply this transform to derive the Harnack inequality for nonnegative solutions in the case where the diffusion matrix is not locally Sobolev. We also obtain a gen...

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Bibliographic Details
Published in:Doklady. Mathematics 2022-11, Vol.106 (2), p.318-321
Main Authors: Bogachev, V. I., Röckner, M., Shaposhnikov, S. V.
Format: Article
Language:English
Subjects:
Existence theorems
Mathematical analysis
Mathematics
Mathematics and Statistics
Transformations (mathematics)
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Summary:— In this note we develop a new analytic version of Zvonkin’s transform of the drift coefficient of a stationary Kolmogorov equation and apply this transform to derive the Harnack inequality for nonnegative solutions in the case where the diffusion matrix is not locally Sobolev. We also obtain a generalization of the known theorem of Hasminskii on existence of a probability solution to the stationary Kolmogorov equation.
ISSN:1064-5624
1531-8362
DOI:10.1134/S1064562422050064