Gevrey Regularity for a Class of Solutions of the Linearized Spatially Homogeneous Boltzmann Equation Without Angular Cutoff

In this paper, we study the Gevrey smoothing property for the non-negative solution of the linearized spatially homogeneous Boltzmann equation. Using pseudo-differential calculus and some techniques of mathematical analysis, we show that in the non-cutoff and non-Maxwellian case with the inverse power law potential, if the solution is Lipschitz continuous on the velocity variable, then it has the local Gevrey regularity.