Conservation laws for conformally invariant variational problems

Inventiones Mathematicae

Volumn 168, Issue 1, 2007, Pages 1-22

  Rivière, Tristan ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33847320537     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-006-0023-0     Document Type: Article

References (31)

1. Bethuel, F.: Un résultat de régularité pour les solutions de l'équation de surfaces courbure moyenne prescrite. C. R. Acad. Sci., Paris, Sér. I, Math. 314(13), 1003-1007 (1992) (French) [A regularity result for solutions to the equation of surfaces of prescribed mean curvature]
2. Bethuel, F.: Weak limits of Palais-Smale sequences for a class of critical functionals. Calc. Var. Partial Differ. Equ. 1(3), 267-310 (1993)
3. Bethuel, F., Ghidaglia, J.-M.: Improved regularity of solutions to elliptic equations involving Jacobians and applications. J. Math. Pures Appl., IX. Sér. 72(5), 441-474 (1993)
4. Bethuel, F., Ghidaglia, J.-M.: Some applications of the coarea formula to partial differential equations. In: Pràstaro, A., Rassias, Th. M. (eds.) Geometry in Partial Differential Equations, pp. 1-17. World Sci. Publishing, River Edge, NJ (1994)
5. Brezis, H., Coron, J.-M.: Multiple solutions of H-systems and Rellich's conjecture. Commun. Pure Appl. Math. 37(2), 149-187 (1984)
6. Choné, P.: A regularity result for critical points of conformally invariant functionals. Potential Anal. 4(3), 269-296 (1995)
7. Coifman, R., Lions, P.-L., Meyer, Y, Semmes, S.: Compensated compactness and Hardy spaces. J. Math. Pures Appl., IX. Sér. 72, 247-286 (1993)
8. Evans, C.: Partial regularity for stationary harmonic maps into spheres. Arch. Ration. Mech. Anal. 116, 101-113 (1991)
9. Frehse, J.: A discontinuous solution of a mildly nonlinear elliptic system. Math. Z. 134, 229-230(1973)
10. Freire A., Müller S., Struwe M.: Weak compactness of wave maps and harmonic maps. Ann. Inst. Henri Poincaré 15(6), 725-754 (1998)
11. Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Ann. Math. Stud., vol. 105. Princeton University Press, Princeton, NJ (1983)
12. Grüter, M.: Conformally invariant variational integrals and the removability of isolated singularities. Manuscr. Math. 47(1-3), 85-104 (1984)
13. Grüter, M.: Regularity of weak H-surfaces. J. Reine Angew. Math. 329, 1-15 (1981)
14. Heinz, E.: Ein Regularitätssatz für schwache Lösungen nichtlinearer elliptischer Systeme. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl. (1), 1-13 (1975) (German)
15. Heinz, E.: Über die Regularität der Lösungen nichtlinearer Wellengleichungen. Nachr. Akad. Wiss. Gött., II Math.-Phys. Kl. (2), 15-26 (1975) (German)
16. Heinz, E.: Über die Regularität schwacher Lösungen nichtlinearer elliptischer Systeme. Nachr. Akad. Wiss. Gött., II Math.-Phys. Kl. (1), 1-15 (1986) (German) [On the regularity of weak solutions of nonlinear elliptic systems]
17. Hélein, F.: Harmonic maps, conservation laws and moving frames. Cambridge Tracts in Mathematics, vol. 150. Cambridge University Press, Cambridge (2002)
18. Hélein, F.: Problèmes invariants par transformations conformes en dimension 2. http://fr.arxiv.org/pdf/math/0101237?
19. Hildebrandt, S.: Nonlinear elliptic systems and harmonic mappings. In: Chern, S.S., Wu, W.T. (eds.) Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, vol. 1-3, pp. 481-615, Beijing, 1980. Science Press, Beijing, 1982
20. Hildebrandt, S.: Quasilinear elliptic systems in diagonal form. Systems of nonlinear partial differential equations, pp. 173-217. Oxford 1982. NATO ASI Ser., Ser C, Math. Phys. Sci., vol. 111. Reidel, Dordrecht, 1983
21. Hildebrandt, S., Widman, K.-O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z. 142, 67-86 (1975)
22. Ladyzhenskaya, O.A., Ural'tseva, N.N.: Linear and Quasilinear Elliptic Equations. Academic Press, New York London (1968)
23. Lin, F.-H., Rivière, T.: Energy quantization for harmonic maps. Duke Math. J. 111(1), 177-193 (2002)
24. Meyer, Y, Rivière, T.: A partial regularity result for a class of stationary Yang-Mills fields in high dimension. Rev. Mat. Iberoam. 19(1), 195-219 (2003)
25. Morrey, C.B. Jr.: Multiple integrals in the calculus of variations. Die Grundlehren der mathematischen Wissenschaften, vol. 130. Springer, New York 1966
26. 1. J. Reine Angew. Math. 412, 20-34 (1990)
27. Shatah, J.: Weak solutions and development of singularities of the SU(2) σ-model. Commun. Pure Appl. Math. 41, 459-469 (1988)
28. Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. (1970)
29. Tartar, L.: Remarks on oscillations and Stokes' equation. In: Frisch, U., et al. (eds.) Macroscopic Modelling of Turbulent Flows, vol. 230, pp. 24-31. Nice, 1984. Lecture Notes Phys., Springer, Berlin (1985)
30. p bounds on curvature. Commun. Math. Phys. 83(1), 31-42 (1982)
31. Wente, H.C.: An existence theorem for surfaces of constant mean curvature. J. Math. Anal. Appl. 26, 318-344 (1969)