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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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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DOI: https://doi.org/10.1007/s00205-015-0948-9