A limiting case for velocity averaging

B. Perthame; P. E. Souganidis

Annales scientifiques de l'École Normale Supérieure (1998)

  • Volume: 31, Issue: 4, page 591-598
  • ISSN: 0012-9593

How to cite

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Perthame, B., and Souganidis, P. E.. "A limiting case for velocity averaging." Annales scientifiques de l'École Normale Supérieure 31.4 (1998): 591-598. <http://eudml.org/doc/82471>.

@article{Perthame1998,
author = {Perthame, B., Souganidis, P. E.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {velocity averaging; transport equations; limiting case; compactness of averages; Calderón-Zygmund theory},
language = {eng},
number = {4},
pages = {591-598},
publisher = {Elsevier},
title = {A limiting case for velocity averaging},
url = {http://eudml.org/doc/82471},
volume = {31},
year = {1998},
}

TY - JOUR
AU - Perthame, B.
AU - Souganidis, P. E.
TI - A limiting case for velocity averaging
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1998
PB - Elsevier
VL - 31
IS - 4
SP - 591
EP - 598
LA - eng
KW - velocity averaging; transport equations; limiting case; compactness of averages; Calderón-Zygmund theory
UR - http://eudml.org/doc/82471
ER -

References

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  1. [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). Zbl0599.35009MR86a:46033
  2. [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). Zbl0655.35075MR89f:35174
  3. [3] M. BÉZARD, Régularité précisée des moyennes dans les équations de transport (Bull. Soc. Math. France, Vol. 122, 1994, pp. 29-76). Zbl0798.35025MR95g:82083
  4. [4] F. BOUCHUT and L. DESVILLETTES, Averaging lemmas without time Fourier transform and applications to discretized kinetic equations. Preprint. Zbl0933.35159
  5. [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). Zbl0876.35088MR98d:82040
  6. [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). Zbl0698.45010MR90k:82045
  7. [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). Zbl0698.35128MR90i:35236
  8. [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). Zbl0763.35014MR92g:35036
  9. [9] P. GÉRARD, Moyennisation et régularité deux-microlocale, (Ann. Sci. Ecole Normale Sup., Vol. 4, 1990, pp. 89-121). Zbl0725.35003MR91g:35068
  10. [10] P. GÉRARD, Microlocal defect measures (Comm. Partial Differential equations, Vol. 16(11), 1991, pp. 1761-1794). Zbl0770.35001MR92k:35027
  11. [11] F. GOLSE, B. PERTHAME and R. SENTISUn résultat de compacité pour les équations du transport... (C. R. Acad. Sci. Paris, Série I, Vol. 301, 1985, pp. 341-344). Zbl0591.45007MR86m:82062
  12. [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). Zbl0652.47031MR89a:35179
  13. [13] P.-L. LIONS, Régularité optimale des moyennes en vitesses (C. R. Acad. Sci. Paris, Série I, Vol. 320, 1995, pp. 911-915). Zbl0827.35110MR96c:35184
  14. [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). Zbl0820.35094MR94d:35100
  15. [15] E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, 1970. Zbl0207.13501MR44 #7280

Citations in EuDML Documents

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  1. Alexis Vasseur, Interface cinétique / fluide : Un modèle simplifié
  2. T. Horsin, S. Mischler, A. Vasseur, On the convergence of numerical schemes for the Boltzmann equation
  3. Pierre-Emmanuel Jabin, Benoît Perthame, Kinetic methods for Line-energy Ginzburg–Landau models
  4. Pierre-Louis Lions, Benoît Perthame, Panagiotis E. Souganidis, Stochastic averaging lemmas for kinetic equations
  5. Florent Berthelin, Stéphane Junca, Des lemmes de moyenne avec un terme de force dans l’équation de transport
  6. Pierre-Emmanuel Jabin, Benoît Perthame, Regularity in kinetic formulations via averaging lemmas
  7. François Golse, New Results in Velocity Averaging
  8. Pierre-Emmanuel Jabin, Benoît Perthame, Regularity in kinetic formulations via averaging lemmas

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