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Abstract
Some theorems of Carleman on the existence and uniqueness of the solutions to the Boltzmann equation are extended to the case ρ(ζ) = ρo ζ−y, with γ ∊ [0,1], where ζ is the relative velocity and a the cross section. Existence is proved in the small when there is a convex surface in the gas, and in the large for a spatially homogeneous gas.