Uncertainty principle and regularity for Boltzmann type equations

Comptes Rendus Mathematique

Volumn 345, Issue 12, 2007, Pages 673-677

  Alexandre, Radjesvarane ^a   Morimoto, Yoshinori ^b   Ukai, Seiji ^c   Xu, Chao Jiang ^d   Yang, Tong ^c,e  

^a IRENav   (France)

^b KYOTO UNIVERSITY   (Japan)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^d UNIVERSITÉ DE ROUEN   (France)

^e SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 36849030327     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2007.10.032     Document Type: Article

References (11)

1. Alexandre R. Integral estimates for linear singular operator linked with Boltzmann operator. Part I: small singularities 0 < ν < 1. Indiana Univ. J. Math. 55-6 (2007)
2. R. Alexandre, Y. Morimoto, S. Ukai, C.-Y. Xu, T. Yang, in preparation
3. Bouchut F. Hypoelliptic regularity in kinetic equations. J. Math. Pure Appl. 81 (2002) 1135-1159
4. Fefferman C. The uncertainty principle. Bull. Amer. Math. Soc. 9 (1983) 129-206
5. Fefferman C., and Phong D.H. The uncertainty principle and sharp Gȧrding inequalities. Comm. Pure. Appl. Math. 34 (1981) 285-331
6. Morimoto Y. The uncertainty principle and hypoelliptic operators. Publ. RIMS Kyoto Univ. 23 (1987) 955-964
7. Morimoto Y. Estimates for degenerate Schrödinger operators and hypoellipticity for infinitely degenerate elliptic operators. J. Math. Kyoto Univ. 32 (1992) 333-372
8. Morimoto Y., and Morioka T. The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators. Bull. Sci. Math. 121 (1997) 507-547
9. Y. Morimoto, S. Ukai, C.-J. Xu, T. Yang, Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff, preprint
10. Y. Morimoto, C.-J. Xu, Hypoellipticity for a class of kinetic equations, J. Math. Kyoto. Univ. 47 (2007), in press
11. Villani C. A review of mathematical topics in collisional kinetic theory. In: Friedlander S., and Serre D. (Eds). Handbook of Mathematical Fluid Dynamics vol. I (2002), North-Holland, Amsterdam 71-305