Regularity of Boltzmann Equation with Cercignani--Lampis Boundary in Convex Domain

The Boltzmann equation is a fundamental kinetic that describes the dynamics of dilute gas. In this paper we study regularity both dynamical and steady in strictly convex domain with Cercignani-Lampis (C-L) boundary condition. C-L condition intermediate reflection law between diffuse specular via two accommodation coefficients. We construct local weighted $C^1$ solution using repeated interaction through characteristic. When assume small fluctuation to wall temperature coefficients, solution.