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Higher order regularity of nonlinear Fokker-Planck PDEs with respect to the measure component
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2021-04-06 , DOI: 10.1016/j.matpur.2021.04.005 Alvin Tse
中文翻译:
非线性Fokker-Planck PDE关于测度分量的高阶正则性
更新日期:2021-04-24
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2021-04-06 , DOI: 10.1016/j.matpur.2021.04.005 Alvin Tse
In this article, we establish a general formula for higher order linear functional derivatives for the composition of an arbitrary smooth functional on the 1-Wasserstein space with the solution of a Fokker-Planck PDE. This formula has important links with the theory of propagation of chaos and mean-field games.
中文翻译:
非线性Fokker-Planck PDE关于测度分量的高阶正则性
在本文中,我们使用Fokker-Planck PDE的解决方案为1-Wasserstein空间上的任意光滑官能团的组成建立了高阶线性官能团导数的一般公式。该公式与混沌和均场博弈的传播理论有着重要的联系。