#### Vol. 14, No. 1, 2021

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The Schauder estimate for kinetic integral equations

### Cyril Imbert and Luis Silvestre

Vol. 14 (2021), No. 1, 171–204
##### Abstract

We establish interior Schauder estimates for kinetic equations with integrodifferential diffusion. We study equations of the form ${f}_{t}+v\cdot {\nabla }_{x}f={\mathsc{ℒ}}_{v}f+c$, where ${\mathsc{ℒ}}_{v}$ is an integrodifferential diffusion operator of order $2s$ acting in the $v$-variable. Under suitable ellipticity and Hölder continuity conditions on the kernel of ${\mathsc{ℒ}}_{v}$, we obtain an a priori estimate for $f$ in a properly scaled Hölder space.

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