A new preprint entitled « The Schauder estimate for kinetic integral equations » is available on arxiv and hal. This is a joint work with Luis Silvestre.
Abstract: We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form ft+v⋅∇xf=Lvf+c, where Lv is an integro-differential diffusion operator of order 2s acting in the v-variable. Under suitable ellipticity and Hölder continuity conditions on the kernel of Lv, we obtain an a priori estimate for f in a properly scaled Hölder space.