Regularity of the Boltzmann equation in convex domains
Date
2017Link to item file
https://arxiv.org/abs/1212.1694v4Dewey
Probabilités et mathématiques appliquéesSujet
BoltzmannJournal issue
Inventiones MathematicaeVolume
207Number
1Publication date
2017Article pages
115-290Publisher
SpringerCollections
Metadata
Show full item recordAuthor
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
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