
We study the nonlinear steady Boltzmann equation in the half space, with phase transition and Dirichlet boundary condition. In particular, we study the regularity of the solution to the half-space problem in the situation that the gas is in contact with its condensed phase. We propose a novel kinetic weight and establish a weighted $C^1$ estimate under the spatial domain $x\in [0,\infty)$, which is unbounded and not strictly convex. Additionally, we prove the $W^{1,p}$ estimate without any weight for $p<2$.
Added references
Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)
Mathematics - Analysis of PDEs, FOS: Mathematics, Analysis of PDEs (math.AP)
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