BV-regularity of the Boltzmann equation in Non-Convex Domains
  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 $\varepsilon-$tubular neighborhood of the singular set. 
Yan Guo, Chanwoo Kim, Daniela Tonon, Ariane Trescases
math.AP