Special Session 17: Nonlinear models in kinetic theory, collective behavior, and fluid dynamics

Regularity Theory for kinetic integro-differential equations

Amelie Loher
University of Cambridge
England
Co-Author(s):    
Abstract:
We discuss regularity estimates for kinetic equations. Concretely, we derive Schauder estimates using ideas from Campanato`s approach for a general class of integro-differential equations. The same method with simplified estimates also works in the non-fractional case for kinetic Fokker-Planck-type equations in either divergence or non-divergence form. In particular our results are applicable to the Boltzmann and Landau equation.