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Journal Articles Analysis & PDE Year : 2020

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.

Dates and versions

hal-01979425 , version 1 (12-01-2019)

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Cite

Cyril Imbert, Luis Silvestre. The Schauder estimate for kinetic integral equations. Analysis & PDE, 2020, 14 (1), pp.171-204. ⟨10.2140/apde.2021.14.171⟩. ⟨hal-01979425⟩
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