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

We establish interior Schauder estimates for kinetic equations with integrodifferential diffusion. We study equations of the form ft + v xf = vf + c, where 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 v, we obtain an a priori estimate for f in a properly scaled Hölder space.

kinetic integrodifferential equations, Schauder estimates
Mathematical Subject Classification
Primary: 35K70, 35R09
Received: 15 January 2019
Accepted: 7 October 2019
Published: 19 February 2021
Cyril Imbert
CNRS and Instituto de Matemática Pura e Aplicada
Rio de Janeiro
Luis Silvestre
Department of Mathematics
The University of Chicago
Chicago, IL
United States