Sobolev Regularity in Neutron Transport Theory

The main purpose of this paper is to extend theW 1 , pregularity results in neutron transport theory, with respect to the Lebesgue measure due to Mokhtar-Kharroubi, (1991), and to abstract measures covering, in particular, the continuous models or multigroup models. The results are obtained for vacuum boundary conditions as well as periodic boundary conditions. H 2 regularity results are derived when the velocity space is endowed with an appropriate class of measures (signed in the multidimensional case).