Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 379491, 22 pages
http://dx.doi.org/10.5402/2012/379491
Research Article

Sobolev Regularity in Neutron Transport Theory

Laboratoire de Mathématiques et Applications, Faculté des Sciences et Techniques, Université Sultan Moulay Slimane, BP 523, Beni-Mellal 23000, Morocco

Received 20 September 2011; Accepted 9 November 2011

Academic Editors: M. Escobedo, K. A. Lurie, and D. X. Zhou

Copyright © 2012 Ahmed Zeghal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to extend the 𝑊1,𝑝 regularity 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. 𝐻2 regularity results are derived when the velocity space is endowed with an appropriate class of measures (signed in the multidimensional case).