BV-Regularity of the Boltzmann Equation in Non-Convex Domains

Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane

Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane (2016), BV-Regularity of the Boltzmann Equation in Non-Convex Domains, Archive for Rational Mechanics and Analysis, 220, 3, p. 1045-1093. 10.1007/s00205-015-0948-9

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1409.0160v1

Date

2016

Journal name

Archive for Rational Mechanics and Analysis

Volume

220

Number

Publisher

Springer

Pages

1045-1093

Publication identifier

10.1007/s00205-015-0948-9

Metadata

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Author(s)

Guo, Yan
Department of Mathematics, Brown University
Kim, Chanwoo

Tonon, Daniela
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Trescases, Ariane

Abstract (EN)

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 ε-tubular neighborhood of the singular set.

Subjects / Keywords

Boltzmann