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

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 $\epsilon -$tubular neighborhood of the singular set.

45 pages, submitted

References in corpus (1)

• Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

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