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arXiv · 2102.04105

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

Jessica Guerand·Cyril Imbert
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Abstract

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{\'e} 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.

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Jessica Guerand, Cyril Imbert. 2021-02-08. Log-transform and the weak Harnack inequality for kinetic Fokker-Planck equations. https://arxiv.org/abs/2102.04105

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