# The Schauder estimate for kinetic integral equations

Abstract : We establish interior Schauder estimates for kinetic equations with integro-differential diffusion. We study equations of the form $f_t + v \cdot \nabla_x f = \mathcal L_v f + c$, where $\mathcal L_v$ is an integro-differential diffusion operator of order $2s$ acting in the $v$-variable. Under suitable ellipticity and H\"older continuity conditions on the kernel of $\mathcal L_v$, we obtain an a priori estimate for $f$ in a properly scaled H\"older space.
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https://hal.archives-ouvertes.fr/hal-01979425
Contributor : Cyril Imbert <>
Submitted on : Saturday, January 12, 2019 - 10:09:01 PM
Last modification on : Thursday, March 26, 2020 - 2:52:06 PM

### Identifiers

• HAL Id : hal-01979425, version 1
• ARXIV : 1812.11870

### Citation

Cyril Imbert, Luis Silvestre. The Schauder estimate for kinetic integral equations. Analysis and PDEs, In press. ⟨hal-01979425⟩

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