Higher order regularity of nonlinear Fokker-Planck PDEs with respect to the measure component

Abstract

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.

arXiv commentFinal version of the paper

References in corpus (2)

• Dynamical aspects of mean field plane rotators and the Kuramoto model
• Propagation of chaos for the Landau equation with moderately soft potentials

Cited by in corpus (4)

• Weak quantitative propagation of chaos via differential calculus on the space of measures
• Central limit theorem over non-linear functionals of empirical measures with applications to the mean-field fluctuation of interacting particle systems
• Uniform in time weak propagation of chaos on the torus
• Weak Error of Dean-Kawasaki Equation with Smooth Mean-Field Interactions