Archive for Rational Mechanics and Analysis

, Volume 220, Issue 3, pp 1045–1093 | Cite as

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

Article

Abstract

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 \({\varepsilon}\)-tubular neighborhood of the singular set.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Department of MathematicsUniversity of WisconsinMadisonUSA
  3. 3.CEREMADEUniversité Paris Dauphine, Place du Maréchal De Lattre De TassignyParisFrance
  4. 4.CMLACachanFrance

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