Hölder regularity of the Boltzmann equation in some non-convex domains

We study Cx,v0,12− Hölder regularity of the Boltzmann equation outside of uniform convex object under specular reflection boundary condition. In particular, this result is different to other boundary conditions in which the solutions can be discontinuous [1] and BV regularity [2]. We define Specular Singularities and introduce Shift method to use ODE argument for Specular Singularities.