Régularité L p précisée des moyennes dans les équations de transport

Max Bezard

Bulletin de la Société Mathématique de France (1994)

  • Volume: 122, Issue: 1, page 29-76
  • ISSN: 0037-9484

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Bezard, Max. "Régularité $L^p$ précisée des moyennes dans les équations de transport." Bulletin de la Société Mathématique de France 122.1 (1994): 29-76. <http://eudml.org/doc/87682>.

@article{Bezard1994,
author = {Bezard, Max},
journal = {Bulletin de la Société Mathématique de France},
keywords = {regularity for velocity averages; transport equation; Sobolev space; Besov spaces},
language = {fre},
number = {1},
pages = {29-76},
publisher = {Société mathématique de France},
title = {Régularité $L^p$ précisée des moyennes dans les équations de transport},
url = {http://eudml.org/doc/87682},
volume = {122},
year = {1994},
}

TY - JOUR
AU - Bezard, Max
TI - Régularité $L^p$ précisée des moyennes dans les équations de transport
JO - Bulletin de la Société Mathématique de France
PY - 1994
PB - Société mathématique de France
VL - 122
IS - 1
SP - 29
EP - 76
LA - fre
KW - regularity for velocity averages; transport equation; Sobolev space; Besov spaces
UR - http://eudml.org/doc/87682
ER -

References

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  1. [1] BERGH (J.) and LÖFSTRÖM (J.). — Interpolation spaces : an introduction. — Springer, 1976. Zbl0344.46071
  2. [2] CHANG (S.Y). — Carleson measure on the bidisc, Ann. of Math., t. 110, 1979, p. 613-620. Zbl0401.28004
  3. [3] CHANG (S.Y) and FEFERMAN (R.). — A continuous version of duality of H1 and BMO on the bidisc, Ann. of Math., t. 112, 1980, p. 179-201. Zbl0451.42014
  4. [4] CHANG (S.Y) and FEFERMAN (R.). — The Calderòn-Zygmund decomposition on product domains, Amer. J. Math., t. 104, 1982, p. 455-468. Zbl0513.42019MR84a:42028
  5. [5] CHANG (S.Y) and FEFERMAN (R.). — Some recents developments in Fourier analysis and Hp-theory on product domains I, Bull. Amer. Math. Soc., t. 12, 1985, p. 1-43. Zbl0557.42007
  6. [6] CHANG (S.Y) and FEFERMAN (R.). — Some recents developments in Fourier analysis and Hp-theory on product domains II, Lecture Notes in Math., t. 1302, 1988, p. 44-51. 
  7. [7] DI PERNA (R.) and LIONS (P.L.). — On the Cauchy problem for Boltzmann equation: global existence and weak stability, Ann. of Math., t. 130, 1989, p. 321-366. Zbl0698.45010MR90k:82045
  8. [8] DI PERNA (R.) and LIONS (P.L.). — Global weak solutions of Vlasov-Maxwell systems, Comm. Pure Appl. Math., t. 42, 1989, p. 729-757. Zbl0698.35128MR90i:35236
  9. [9] DI PERNA (R.) and LIONS (P.L.). — On Fokker-Planck-Boltzmann equation, Comm. Math. Phys., t. 120, 1988, p. 1-23. Zbl0671.35068MR90b:35203
  10. [10] DI PERNA (R.) and LIONS (P.L.). — Solutions globales d'équations du type Vlasov-Poisson, CR Acad. Sci. Paris, t. I, 307, 1988, p. 655-658. Zbl0682.35022MR89k:35202
  11. [11] DI PERNA (R.), LIONS (P.L.) and MEYER (Y.). — Lp regularity of velocity averages, Ann. Inst. H. Poincaré Anal., t. 8, 1991, p. 271-288. Zbl0763.35014MR92g:35036
  12. [12] FEFFERMAN (C.) and STEIN (E.M.). — Hp spaces of several variables, Acta Math., t. 129, 1972, p. 137-193. Zbl0257.46078MR56 #6263
  13. [13] FEFFERMAN (R.). — Bounded mean oscillation on the polydisc, Ann. of Math., t. 110, 1979, p. 395-406. Zbl0429.32016MR81c:32016
  14. [14] FEFFERMAN (R.). — Singular integrals on product domains, Bull. Amer. Math. Soc., t. 4, 1981, p. 195-201. Zbl0466.42007MR83i:42014
  15. [15] FEFFERMAN (R.). — Singular integrals on product Hp spaces, Rev. Mat. Iberoamericana, t. 1, 1985, p. 25-31. Zbl0613.42019MR88f:42034
  16. [16] FEFFERMAN (R.). — Fourier analysis in several parameters, Rev. Mat. Iberoamericana, t. 2, 1986, p. 89-98. Zbl0641.42018MR88m:42024
  17. [17] FEFFERMAN (R.). — Harmonic analysis on product spaces, Ann. of Math., t. 126, 1987, p. 109-130. Zbl0644.42017MR90e:42030
  18. [18] FEFFERMAN (R.). — Ap weights and singular integrals, Amer. J. Math., t. 110, 1988, p. 975-987. Zbl0665.42020MR90b:42033
  19. [19] FEFFERMAN (R.) and STEIN (E.M.). — Singular integrals on product domains, Bull. Amer. Math. Soc., t. 4, 1981, p. 195-201. Zbl0466.42007MR83i:42014
  20. [20] GÉRARD (P.). — Moyennes de solutions d'équations aux dérivées partielles, Journées EDP St Jean-de-Monts, exposé XI, École Polytechnique France 1987. 
  21. [21] GÉRARD (P.). — Compacité par compensation et régularité 2-microlocale, Séminaire équations aux dérivées partielles, exposé VI, École Polytechnique France 1988-1989. Zbl0707.35032
  22. [22] GÉRARD (P.). — Moyennisation et régularité 2-microlocale, Ann. Sci. École Norm. Sup., t. 23, 1990, p. 89-121. Zbl0725.35003MR91g:35068
  23. [23] GOLSE (F.), LIONS (P.L.), PERTHAME (B.) and SENTIS (R.). — Regularity of the moments of the solution of a transport equation, J. Funct. Anal., t. 76, 1988, p. 110-125. Zbl0652.47031MR89a:35179
  24. [24] GOLSE (F.), PERTHAME (B.) et SENTIS (R.). — Un résultat de compacité pour les équations de transport et applications au calcul de la limite de la valeur propre principale d'un opérateur de transport, C.R. Acad. Sci. Paris, t. 301, 1985, p. 341-344. Zbl0591.45007MR86m:82062
  25. [25] GUNDY (R.F.) and STEIN (E.M.). — Hp theory for the polydisc, Proc. Nat. Acad. Sci. U.S.A., t. 76, 1979, p. 1026-1029. Zbl0405.32002MR80j:32012
  26. [26] LIN (K.C.). — Interpolation between Hardy spaces on the bidisc, Studia Math., t. 84, 1984, p. 85-97. Zbl0626.46060MR88f:46057
  27. [27] PEETRE (J.). — New thoughts on Besov spaces. — Mimeographed Notes, Duke University, 1973. 
  28. [28] STEIN (E.M.). — Singular integrals and differentiability properties of functions. — Princeton Univ. Press, 1971. Zbl0207.13501
  29. [29] TORCHINSKY (A.). — Real variable methods in harmonic analysis. — Academic Press, 1986. Zbl0621.42001MR88e:42001
  30. [30] TRIEBEL (H.). — Theory of function spaces. — Birkhaüser, 1983. 
  31. [31] WOLF (E.). — Note on interpolation spaces, Lecture Note in Math., t. 908, 1982, p. 199-205. Zbl0517.46054MR83f:46082
  32. [32] BEZARD (M.). — Precised Lp regularity for averages in transport equations II, à paraître. 

Citations in EuDML Documents

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  1. Albert Cohen, Ondelettes, espaces d’interpolation et applications
  2. B. Perthame, P. E. Souganidis, A limiting case for velocity averaging
  3. Pierre-Emmanuel Jabin, Some regularizing methods for transport equations and the regularity of solutions to scalar conservation laws
  4. Benoît Perthame, Un cas limite de lemmes de compacité en moyenne motivé par la formulation cinétique de systèmes hyperboliques
  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. Pierre-Emmanuel Jabin, Benoît Perthame, Regularity in kinetic formulations via averaging lemmas

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