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Regularity of the Boltzmann Equation in Convex Domains

Pré-print du CMLA 2013-01 - version du 24 janvier 2013

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Auteurs : Y. Guo, C. Kim, D. Tonon, A. Trescases

Abstract :
Consider the Boltzmann equation in a strictly convex domain with the diffuse boundary condition. We construct W^{1,p} solutions for 1< p<2. With the aid of a distance function toward the grazing set, we construct weighted W^{1,p} solutions for p in [2,infinity] and classical C^{1} solutions away from the grazing set.
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