LOG-TRANSFORM AND THE WEAK HARNACK INEQUALITY FOR KINETIC FOKKER-PLANCK EQUATIONS
LOG-TRANSFORM AND THE WEAK HARNACK INEQUALITY FOR KINETIC FOKKER-PLANCK EQUATIONS
复制标题
动态福克-普朗克方程的对数变换和弱哈纳克不等式
DOI：
10.1017/s1474748022000160
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发表时间：
2021
影响因子：
0.9
通讯作者：
C. Imbert
中科院分区：
文献类型：
--
作者：
Jessica Guerand;C. Imbert
本文讨论具有本质有界系数的动力学Fokker-Planck方程。通过考虑非负超解的对数变换和引入S. N. Kružkov（1963）.这样的结果依赖于一个新的弱Poincaré不等式，该不等式与W. Wang和L. Zhang在一系列关于超抛物方程的作品中（2009，2011，2017）。这个功能的不等式是结合了一个经典的覆盖参数最近改编的L。Silvestre和第二作者（2020）对动力学方程。
Abstract This article deals with kinetic Fokker–Planck equations with essentially bounded coefficients. A weak Harnack inequality for nonnegative super-solutions is derived by considering their log-transform and adapting an argument due to S. N. Kružkov (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.