This paper focuses on the study of existence and uniqueness of distributional
and classical solutions to the Cauchy Boltzmann problem for the soft potential
case assuming Sn−1 integrability of the angular part of the collision
kernel (Grad cut-off assumption). For this purpose we revisit the
Kaniel--Shinbrot iteration technique to present an elementary proof of
existence and uniqueness results that includes large data near a local
Maxwellian regime with possibly infinite initial mass. We study the propagation
of regularity using a recent estimate for the positive collision operator given
in [3], by E. Carneiro and the authors, that permits to study such propagation
without additional conditions on the collision kernel. Finally, an
Lp-stability result (with 1≤p≤∞) is presented assuming the
aforementioned condition.Comment: 19 page