Lois de conservation et régularité par compensation pour les systèmes antisymétriques et les surfaces de Willmore [d'après Tristan Rivière]

Serfaty, Sylvia

Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1024, 14 p.

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MR 2906360 | Zbl 1360.58013

@incollection{AST_2011__339__357_0,
     author = {Serfaty, Sylvia},
     title = {Lois de conservation et r\'egularit\'e par compensation pour les syst\`emes antisym\'etriques et les surfaces de Willmore [d'apr\`es Tristan Rivi\`ere]},
     booktitle = {S\'eminaire Bourbaki, volume 2009/2010, expos\'es 1012-1026},
     author = {Collectif},
     series = {Ast\'erisque},
     note = {talk:1024},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {339},
     year = {2011},
     zbl = {1360.58013},
     mrnumber = {2906360},
     language = {fr},
     url = {archive.numdam.org/item/AST_2011__339__357_0/}
}

Serfaty, Sylvia. Lois de conservation et régularité par compensation pour les systèmes antisymétriques et les surfaces de Willmore [d'après Tristan Rivière], dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1024, 14 p. http://archive.numdam.org/item/AST_2011__339__357_0/

Bibliographie

[1] D. R. Adams - A note on Riesz potentials, Duke Math. J. 42 (1975), p. 765-778. | Article | MR 458158 | Zbl 0336.46038

[2] Y. Bernard & T. Rivière - Local Palais-Smale sequences for the Willmore functional, prépublication arXiv : 0904.0360. | Article | MR 2843242 | Zbl 1245.53051

[3] F. Bethuel - Un résultat de régularité pour les solutions de l'équation de surfaces à courbure moyenne prescrite, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), p. 1003-1007. | MR 1168525 | Zbl 0795.35024

[4] F. Bethuel, On the singular set of stationary harmonic maps, Manuscripta Math. 78 (1993), p. 417-443. | Article | EuDML 155819 | MR 1208652 | Zbl 0792.53039

[5] W. Blaschke - Vorlesungen über differentiale Geometrie III, Springer, 1929.

[6] R. R. Coifman, P.-L. Lions, Y. Meyer & S. Semmes - Compensated compactness and hardy spaces, J. Math. Pures Appl. 72 (1993), p. 247-286. | MR 1225511 | Zbl 0864.42009

[7] R. R. Coifman, R. Rochberg & G. Weiss - Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), p. 611-635. | Article | MR 412721 | Zbl 0326.32011

[8] F. Da Lio & T. Rivière - $3$ -commutator estimates and the regularity of $1 / 2$ -harmonic maps into spheres, prépublication arXiv : 0901.2533. | MR 2783309 | Zbl 1241.35035

[9] F. Da Lio & T. Rivière, The regularity of solutions to critical non-local Schrödinger systems on the line with antisymmetric potential and applications, prépublication.

[10] L. C. Evans - Partial regularity for stationary harmonic maps into spheres, Arch. Rational Mech. Anal. 116 (1991), p. 101-113. | Article | MR 1143435 | Zbl 0754.58007

[11] J. Frehse - A discontinuous solution of a mildly nonlinear elliptic system, Math. Z. 134 (1973), p. 229-230. | Article | EuDML 171982 | MR 344673 | Zbl 0267.35038

[12] M. Grüter - Conformally invariant variational integrals and the removability of isolated singularities, Manuscripta Math. 47 (1984), p. 85-104. | Article | EuDML 155006 | MR 744314 | Zbl 0543.49020

[13] F. Hélein - Harmonic maps, conservation laws and moving frames, 2e éd., Cambridge Tracts in Math., vol. 150, Cambridge Univ. Press, 2002. | MR 1913803 | Zbl 1010.58010

[14] T. Rivière - Conservation laws for conformally invariant variational problems, Invent. Math. 168 (2007), p. 1-22. | Article | MR 2285745 | Zbl 1128.58010

[15] T. Rivière, Analysis aspects of Willmore surfaces, Invent. Math. 174 (2008), p. 1-45. | Article | MR 2430975 | Zbl 1155.53031

[16] T. Rivière, en préparation.

[17] L. Simon - Existence of surfaces minimizing the Willmore functional, Comm. Anal. Geom. 1 (1993), p. 281-326. | Article | MR 1243525 | Zbl 0848.58012

[18] G. Thomsen - Über konforme Geometrie, I. Grundlagen der konformen Flächentheorie, Abh. Math. Sem. Hamburg 3 (1923), p. 31-56. | Article | JFM 49.0530.02 | MR 3069418

[19] K. K. Uhlenbeck - Connections with $L^{p}$ bounds on curvature, Comm. Math. Phys. 83 (1982), p. 31-42. | Article | MR 648356 | Zbl 0499.58019

[20] H. C. Wente - An existence theorem for surfaces of constant mean curvature, J. Math. Anal. Appl. 26 (1969), p. 318-344. | Article | MR 243467 | Zbl 0181.11501

[21] T. J. Willmore - Riemannian geometry, Oxford Science Publications, The Clarendon Press Oxford Univ. Press, 1993. | MR 1261641 | Zbl 0797.53002