2021/02/08 by Jessica Guerand, Cyril Imbert, Guerand, Jessica +1 · 2 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Nonlinear Partial Differential Equations #Statistical Mechanics and Entropy
paper · doi:10.48550/arxiv.2102.04105
openalex publication_date 2021/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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 Poincaré 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.