A real space method for averaging lemmas

Journal des Mathematiques Pures et Appliquees

Volumn 83, Issue 11, 2004, Pages 1309-1351

  Jabin, Pierre Emmanuel ^a   Vega, Luis ^b  

^a ÉCOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

Averaging lemmas; Dispersion estimates; Regularizing effects; X ray transform

Indexed keywords

EID: 5744245712     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2004.03.004     Document Type: Article

References (32)

1. Ambrosio L. De Lellis C. Mantegazza C. Line energies for gradient vector fields in the plane Calc. Var. Partial Differential Equations 9 1999 327-355
2. Bergh J. Löfström J. Interpolation Spaces. An Introduction A Ser. Comprehensive Stud. Math. vol. 223 1976 Springer-Verlag Berlin-New York
3. p précisée des moyennes dans les équations de transport Bull. Soc. Math. France 122 1994 29-76
4. Bouchut F. Hypoelliptic regularity in kinetic equations J. Math. Pures Appl. (9) 81 2002 1135-1159
5. Bouchut F. Desvillettes L. Averaging lemmas without time Fourier transform and applications to discretized kinetic equations Proc. Roy. Soc. Edinburgh Sect. A 129 1999 19-36
6. Bouchut F. Golse F. Pulvirenti M. Kinetic Equations and Asymptotic Theory Ser. Appl. Math. 2000 Gauthiers-Villars Paris
7. Brenier Y. Corrias L. A kinetic formulation for multi-branch entropy solutions of scalar conservation laws Ann. Inst. H. Poincaré, Anal. Non Linéaire 15 1998 169-190
8. Christ M. Estimates for the k-plane transform Indiana Univ. Math. J. 33 6 1984 891-910
9. DeVore R. Petrova G.P. The averaging lemma J. Amer. Math. Soc. 14 2001 279-296
10. DiPerna R. Lions P.L. Global weak solutions of Vlasov-Maxwell systems Comm. Pure Appl. Math. 42 1989 729-757
11. p regularity of velocity averages Ann. Inst. H. Poincaré Anal. Non Linéaire 8 1991 271-287
12. Duoandikoetxea J. Oruetxebarria O. Mixed norm inequalities for directional operators associated to potentials Potential Anal. 15 2001 273-283
13. Gérard P. Microlocal defect measures Comm. Partial Differential Equations 16 1991 1761-1794
14. Golse F. Quelques résultats de moyennisation pour les équations aux dérivées partielles Fascicolo speciale 1988, Hyperbolic equations Rend. Sem. Mat. Univ. Politec. Torino 1987 101-123
15. Golse F. Lions P.L. Perthame B. Sentis R. Regularity of the moments of the solution of a transport equation J. Funct. Anal. 26 1988 110-125
16. Golse F. Perthame B. Sentis R. 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 C. R. Acad. Sci. Paris Sér. I Math. 301 1985 341-344
17. Hwang S. Tzavaras A. Kinetic decomposition of approximate solutions to conservation laws: applications to relaxation and diffusion-dispersion approximations Comm. Partial Differential Equations 27 5-6 2002 1229-1254
18. Jabin P.E. Perthame B. Compactness in Ginzburg-Landau energy by kinetic averaging Comm. Pure Appl. Math. 54 9 2001 1096-1109
19. Jabin P.E. Perthame B. Regularity in kinetic formulations via averaging lemmas ESAIM Control Optim. Calc. Var. 8 2002 761-774
20. Lions J.L. Peetre J. Sur une classe d'espaces d'interpolation Inst. Hautes Études Sci. Publ. Math. 19 1964 5-68
21. Lions P.L. Régularité optimale des moyennes en vitesse C. R. Acad. Sci. Sér. I Math. 320 1995 911-915
22. Lions P.L. Régularité optimale des moyennes en vitesse C. R. Acad. Sci. Sér. I Math. 326 1998 945-948
23. Lions P.L. Perthame B. Tadmor E. A kinetic formulation of multidimensional scalar conservation laws and related questions J. Amer. Math. Soc. 7 1994 169-191
24. Lions P.L. Perthame B. Tadmor E. Kinetic formulation of the isentropic gas dynamics and p-systems Comm. Math. Phys. 163 1994 415-431
25. Oleinik O.A. On Cauchy's problem for nonlinear equations in a class of discontinuous functions Dokl. Akad. Nauk SSSR (N.S.) 95 1954 451-454
26. Perthame B. Kinetic Formulations of Conservation Laws Oxford Ser. Math. Appl. 2002 Oxford Univ. Press London
27. Perthame B. Souganidis P.E. A limiting case for velocity averaging Ann. Sci. École Norm. Sup. (4) 31 1998 591-598
28. Portilheiro M. Compactness of velocity averages Indiana Univ. Math. J. 51 2002 357-379
29. T. Rivière, S. Serfaty, Compactness, kinetic formulation, and entropies for a problem related to micromagnetics, Preprint, 2001
30. Vasseur A. Time regularity for the system of isentropic gas dynamics with γ=3 Comm. Partial Differential Equations 24 11-12 1999 1987-1997
31. Westinckenberg M. Some new velocity averaging results SIAM J. Math. Anal. 33 5 2002 1007-1032
32. Wolff T. A mixed norm estimate for the X-ray transform Rev. Mat. Iberoamericana 14 3 1998 561-600