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

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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Correspondence to C. Kim.

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Communicated by L. Saint-Raymond

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Guo, Y., Kim, C., Tonon, D. et al. BV-Regularity of the Boltzmann Equation in Non-Convex Domains. Arch Rational Mech Anal 220, 1045–1093 (2016). https://doi.org/10.1007/s00205-015-0948-9

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Keywords

  • Boltzmann Equation
  • Radon Measure
  • Trace Theorem
  • Duhamel Formula
  • Diffuse Boundary Condition