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Regularity of the Boltzmann equation in convex domains

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Date
2017
Link to item file
https://arxiv.org/abs/1212.1694v4
Dewey
Probabilités et mathématiques appliquées
Sujet
Boltzmann
Journal issue
Inventiones Mathematicae
Volume
207
Number
1
Publication date
2017
Article pages
115-290
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00222-016-0670-8
URI
https://basepub.dauphine.fr/handle/123456789/15797
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Guo, Yan
229445 Division of Applied Mathematics
Kim, Chanwoo
Tonon, Daniela
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Trescases, Ariane
62 Centre de Mathématiques et de Leurs Applications [CMLA]
Type
Article accepté pour publication ou publié
Abstract (EN)
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical C1 solutions away from the grazing set for all boundary conditions. For the diffuse boundary condition, we construct W1,p solutions for 1

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