Regularity of solutions to the spatially homogeneous Boltzmann equation for non Maxwellian molecules without angular cutoff

In this paper, we use the pseudo-differential calculus to analyze the smoothing property of weak solutions to the spatially homogeneous Boltzmann equation. Precisely, we show that for the non-Maxwellian molecules with Debye–Yukawa potential, if the positive weak solution is Lipschitz continuous in the velocity variable, then it lies in the Sobolev space Hloc+∞(R3) and hence it is automatically smooth.