Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations

This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering their Log-transform and following S. N. Kruzhkov (1963). Such a result rests on a new weak Poincar{é} inequality sharing...

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Guerand, Jessica, Imbert, Cyril
Format: Article
Language:English
Subjects:
Fokker-Planck equation
Inequality
Kinetic equations
Mathematical analysis
Online Access:Get full text
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Summary:This article deals with kinetic Fokker-Planck equations with essentially bounded coefficients. A weak Harnack inequality for non-negative super-solutions is derived by considering their Log-transform and following S. N. Kruzhkov (1963). Such a result rests on a new weak Poincar{é} inequality sharing similarities with the one introduced by W. Wang and L. Zhang in a series of works about ultraparabolic equations (2009, 2011, 2017). This functional inequality is combined with a classical covering argument recently adapted by L. Silvestre and the second author (2020) to kinetic equations.
ISSN:2331-8422