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 ε-tubular neighborhood of the singular set.
BV-Regularity of the Boltzmann Equation in Non-Convex Domains
D. Tonon;
2016
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 ε-tubular neighborhood of the singular set.
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