A limiting case for velocity averaging
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 4, pp. 591-598. 
@article{ASENS_1998_4_31_4_591_0,
     author = {Perthame, B. and Souganidis, P. E.},
     title = {A limiting case for velocity averaging},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {591--598},
     publisher = {Elsevier},
     volume = {Ser. 4, 31},
     number = {4},
     year = {1998},
     doi = {10.1016/s0012-9593(98)80108-0},
     mrnumber = {99h:82064},
     zbl = {0956.45010},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(98)80108-0/}
}
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Perthame, B.; Souganidis, P. E. A limiting case for velocity averaging. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 31 (1998) no. 4, pp. 591-598. doi : 10.1016/s0012-9593(98)80108-0. http://www.numdam.org/articles/10.1016/s0012-9593(98)80108-0/

[1] V. I. Agoshkov, Spaces of functions with differential-difference characteristics and smoothness of solutions of the transport equation (Soviet Math. Dokl., Vol. 29, 1984, pp. 662-666). | MR | Zbl

[2] C. Bardos, F. Golse, B. Perthame and R. Sentis, The nonaccretive radiative transfer equations. Existence of solutions and Rosseland approximation (J. Funct. Anal., Vol. 77, 1988, pp. 434-460). | MR | Zbl

[3] M. Bézard, Régularité précisée des moyennes dans les équations de transport (Bull. Soc. Math. France, Vol. 122, 1994, pp. 29-76). | Numdam | MR | Zbl

[4] F. Bouchut and L. Desvillettes, Averaging lemmas without time Fourier transform and applications to discretized kinetic equations. Preprint.

[5] L. Desvillettes and S. Mischler, About the splitting algorithms for Boltzmann and BGK equations (Math. Model. Meth. Appl. Sc., Vol. 6, 1996, pp. 1079-1101). | MR | Zbl

[6] R. J. Diperna and P.-L. Lions, On the Cauchy problem for the Boltzmann Equation : global existence and weak stability results (Ann. Math., Vol. 130, 1989, pp. 321-366). | MR | Zbl

[7] R. J. Diperna and P.-L. Lions, Global weak solutions of Vlasov-Maxwell systems (Comm. Pure Appl. Math., Vol. 42, 1989, pp. 729-757). | MR | Zbl

[8] R. J. Diperna, P.-L. Lions and Y. Meyer, Lp regularity of velocity averages (Ann. Inst. H. Poincaré Ann. Non Linéaire, Vol. 8, 1991, pp. 271-287). | Numdam | MR | Zbl

[9] P. Gérard, Moyennisation et régularité deux-microlocale, (Ann. Sci. Ecole Normale Sup., Vol. 4, 1990, pp. 89-121). | Numdam | MR | Zbl

[10] P. Gérard, Microlocal defect measures (Comm. Partial Differential equations, Vol. 16(11), 1991, pp. 1761-1794). | MR | Zbl

[11] F. Golse, B. Perthame and R. Sentis Un résultat de compacité pour les équations du transport... (C. R. Acad. Sci. Paris, Série I, Vol. 301, 1985, pp. 341-344). | MR | Zbl

[12] F. Golse, P.-L. Lions, B. Perthame and R. Sentis, Regularity of the moments of the solution of a transport equation (J. Funct. Anal., Vol. 76, 1988, pp. 110-125). | MR | Zbl

[13] P.-L. Lions, Régularité optimale des moyennes en vitesses (C. R. Acad. Sci. Paris, Série I, Vol. 320, 1995, pp. 911-915). | MR | Zbl

[14] P. L. Lions, B. Perthame and E. Tadmor, A kinetic formulation of multidimensional scalar conservation laws and related equations (J. of AMS, Vol. 7, 1994, pp. 169-191). | MR | Zbl

[15] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. | MR | Zbl

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