BV-Regularity of the Boltzmann equation in non-convex domains

Yan Guo (1) , Chanwoo Kim (2) , Daniela Tonon (3) , Ariane Trescases (4)

1 Department of Mathematics
2 Department of Mathematics [Madison]
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 CMLA - Centre de Mathématiques et de Leurs Applications

We consider the Boltzmann equation in a general non-convex domain with the diffuse boundary condition. We establish optimal BV estimates for such solutions. Our method consists of a new W^1,1 trace estimate for the diffuse boundary condition and a delicate construction of an "epsilon-tubular" neighborhood of the singular set.

Domaines: Equations aux dérivées partielles [math.AP]

Yan Guo, Chanwoo Kim, Daniela Tonon, Ariane Trescases. BV-Regularity of the Boltzmann equation in non-convex domains . Archive for Rational Mechanics and Analysis, 2016, 220 (3), pp.1045-1093. ⟨10.1007/s00205-015-0948-9⟩. ⟨hal-01250819⟩