Table of Contents
ISRN Mathematical Analysis
Volume 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.

Linked References

  1. M. Cessenat, “Théorèmes de trace Lp pour des espaces de fonctions de la neutronique,” Comptes Rendus des Séances de l'Académie des Sciences: Série I, vol. 299, no. 16, pp. 831–834, 1984. View at Google Scholar
  2. M. Cessenat, “Théorèmes de trace pour des espaces de fonctions de la neutronique,” Comptes Rendus des Séances de l'Académie des Sciences: Série I, vol. 300, no. 3, pp. 89–92, 1985. View at Google Scholar
  3. R. Dautray and J. L. Lions, Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, vol. 9, Masson, Paris, France, 1985.
  4. W. Greenberg, C. Van der Mee, and V. Protopopescu, Boundary Value Problems in Abstract Kinetic Theory, vol. 23 of Operator Theory: Advances and Applications, Birkhäuser, Basel, Switzerland, 1987.
  5. M. Mokhtar-Kharroubi, “W1,p regularity in transport theory,” Mathematical Models & Methods in Applied Sciences, vol. 1, no. 4, pp. 477–499, 1991. View at Publisher · View at Google Scholar
  6. V. Caselles and M. Mokhtar-Kharroubi, “On the approximation of the leading eigenelements for a class of transport operators,” Transport Theory and Statistical Physics, vol. 23, no. 4, pp. 501–516, 1994. View at Publisher · View at Google Scholar
  7. M. Mokhtar-Kharroubi, “Régularité de Sobolev en théorie du transport et applications aux problèmes d'approximation,” Comptes Rendus de l'Académie des Sciences. Série I, vol. 314, no. 1, pp. 25–29, 1992. View at Google Scholar
  8. M. Mokhtar-Kharroubi, “On the approximation of a class of transport equations,” Transport Theory and Statistical Physics, vol. 22, no. 4, pp. 561–570, 1993. View at Publisher · View at Google Scholar
  9. F. Golse, P.-L. Lions, B. Perthame, and R. Sentis, “Regularity of the moments of the solution of a transport equation,” Journal of Functional Analysis, vol. 76, no. 1, pp. 110–125, 1988. View at Publisher · View at Google Scholar
  10. V. I. Agoshkov, “Spaces of functions with differential-difference characteristics and smoothness of solutions of the transport equation,” Soviet Mathematics—Doklady, vol. 29, pp. 662–666, 1984. View at Google Scholar
  11. F. Golse, B. Perthame, and R. Sentis, “Un résultat de compacité pour les équations de transport et application au calcul de la limite de la valeur propre principale d'un opérateur de transport,” Comptes Rendus des Séances de l'Académie des Sciences. Série I, vol. 301, no. 7, pp. 341–344, 1985. View at Google Scholar
  12. P. Gérard, “Moyennes de solutions d’équations aux dérivées partielles,” in Proceedings of the Séminaire Équations aux Dérivées Partielles et Applications (EDP '1986-1987), École Polytechnique, Palaiseau, France, 1987.
  13. R. J. DiPerna, P.-L. Lions, and Y. Meyer, “LP regularity of velocity averages,” Annales de l'Institut Henri Poincaré: Analyse Non Linéaire, vol. 8, no. 3-4, pp. 271–287, 1991. View at Google Scholar
  14. M. Bézard, “Régularité Lp précisée des moyennes dans les équations de transport,” Bulletin de la Société Mathématique de France, vol. 122, no. 1, pp. 29–76, 1994. View at Google Scholar
  15. P.-L. Lions, “Régularité optimale des moyennes en vitesses,” Comptes Rendus de l'Académie des Sciences. Série I, vol. 320, no. 8, pp. 911–915, 1995. View at Google Scholar
  16. P.-L. Lions, “Régularité optimale des moyennes en vitesses. II,” Comptes Rendus de l'Académie des Sciences. Série I, vol. 326, no. 8, pp. 945–948, 1998. View at Publisher · View at Google Scholar
  17. C. Bardos, F. Golse, B. Perthame, and R. Sentis, “The nonaccretive radiative transfer equations: existence of solutions and Rosseland approximation,” Journal of Functional Analysis, vol. 77, no. 2, pp. 434–460, 1988. View at Publisher · View at Google Scholar
  18. R. J. DiPerna and P.-L. Lions, “On the Cauchy problem for Boltzmann equations: global existence and weak stability,” Annals of Mathematics, vol. 130, no. 2, pp. 321–366, 1989. View at Publisher · View at Google Scholar
  19. M. Mokhtar-Kharroubi, Mathematical Topics in Neutron Transport Theory, vol. 46 of Series on Advances in Mathematics for Applied Sciences, World Scientific, River Edge, NJ, USA, 1997.
  20. M. Mokhtar-Kharroubi and A. Zeghal, “Inverse problems for periodic transport equations,” Annales de la Faculté des Sciences de Toulouse 6, vol. 9, no. 3, pp. 487–507, 2000. View at Google Scholar
  21. E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, no. 30, Princeton University Press, Princeton, NJ, USA, 1970.
  22. F. Natterer, The Mathematics of Computerized Tomography, Wiley-Teubner, Stuttgart, Germany, 1986.