BV-regularity of the Boltzmann equation in Non-Convex Domains

2014/08/30 by Yan Guo, Chanwoo Kim, Daniela Tonon +1 · 1 citation
Mathematics · #math.AP

paper · pdf · doi:10.1007/s00205-015-0948-9

published as Archive for Rational Mechanics and Analysis June 2016, Volume 220, Issue 3, pp 1045-1093, https://rdcu.be/56Iq · 45 pages, submitted

arxiv created 2014/08/30 · arxiv updated 2018/09/11

Abstract

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 and an ε-tubular neighborhood of the singular set.

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