A Revision on Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials

This short note complements the recent paper of the authors [2]. We revisit the results on propagation of regularity and stability using Lp estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show here the correct range of exponents. We require a Lebesgue’s exponent α > 1 in the angular part of the collision kernel in order to obtain finiteness in some constants involved in the regularity and stability estimates. As a consequence the Lp regularity associated to the Cauchy problem of the space inhomogeneous Boltzmann equation holds for a finite range of p ≥ 1 explicitly determined.