The reconstruction problem for the Euler-Poisson system in cosmology

Archive for Rational Mechanics and Analysis

Volumn 179, Issue 2, 2006, Pages 153-216

  Loeper, Grégoire ^a  

^a EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32544455667     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-005-0384-3     Document Type: Article

References (23)

1. BARLES, G.: Solutions de viscosité des équations de Hamilton-Jacobi. Mathématiques & Applications [Mathematics & Applications] 17 Springer-Verlag, Paris, 1994
2. BEC, J.: Particules Singularités et Turbulence. Phd thesis, Thèse de l'Université Pierre et Marie Curie, 2002
3. BENAMOU, J.-D., BRENIER, Y.: A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem. Numer. Math. 84, 375-393 (2000)
4. BOUCHITTÉ, O., BUTTAZZO, G., FRAGALÀ, I.: Convergence of Sobolev spaces on varying manifolds. J. Geom. Anal. 11, 399-422 (2001)
5. BRENIER, Y.: Polar factorization and monotone rearrangement of vector-valued functions. Commun. Pure Appl. Math. 44, 375-417 (1991)
6. BRENIER, Y.: A homogenized model for vortex sheets. Arch. Ration. Mech. Anal. 138, 319-353 (1997)
7. BRENIER, Y.: Minimal geodesics on groups of volume-preserving maps and generalized solutions of the Euler equations. Commun. Pure Appl. Math. 52, 411-452 (1999)
8. Brenier,Y., FRISCH, U., HÉNON, M., LOEPER, G., MATARRESE, S., MOHAYAEE, R., SOBOLEVSKII, A.: Reconstruction of the early Universe as a convex optimization problem. Mon. Not. R. Astron. Soc. 346, 501-524 (2003)
9. BRÉZIS, H.: Analyse fonctionnelle. Collection Mathématiques Appliquées pour la Maî trise. [Collection of Applied Mathematics for the Master's Degree]. Masson, Paris, 1983 Théorie et applications. [Theory and applications]
10. CAMALET, E.: Méthodes de couplage Euler-Lagrange pour les équations d'Euler-Poisson. PhD thesis, Université de Paris 6, 1995
11. DIPERNA, R.J., LIONS, P.-L.: Ordinary differential equations transport theory and Sobolev spaces. Invent. Math. 98, 511-547 (1989)
12. EVANS, L.C.: Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998
13. EVANS, L.C.: Some new PDE method for weak KAM theory. Calc. Var. Partial Differential Equations 17, 159-177 (2003)
14. EVANS, L.C., GOMES, D.: Effective Hamiltonians and averaging for Harmiltonian dynamics. I Arch. Ration. Mech. Anal. 157, 1-33 (2001)
15. 1 critical subsolution of the Hamilton-Jacobi equation. Invent. Math. 155, 363-388 (2004)
16. FRISCH, U., MATARRESE, S., MOHAYAEE, R., SOBOLEVSKI, A.: A reconstruction of the initial conditions of the Universe by optimal mass transportation. Nature 417, 260-262 (2002)
17. GILBARG, D., TRUDINGER, N.S.: Elliptic partial differential equations of second order, volume 224 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, second edition, 1983
18. GUIONNET, A.: First order asymptotics of matrix integrals; a rigorous approach towards the understanding of matrix models. Commun. Math. Phys. 244, 527-569 (2004)
19. HUTCHINSON, J.E.: Second fundamental form for varifolds and the existence of surfaces minimising curvature. Indiana Univ. Math. J. 35, 45-71 (1986)
20. LIONS, J.-L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, 1969
21. MCCANN, R.J.: A convexity principle for interacting gases. Adv. Math. 128, 153-179 (1997)
22. OTTO, F.: The geometry of dissipative evolution equations: the porous medium equation. Commun. Partial Differential Equations 26, 101-174 (2001)
23. VILLANI, C.: Topics in optimal transportation, volume 58 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2003