@article{JEDP_2006____A9_0, author = {Rivi\`ere, Tristan}, title = {Lois de conservation pour les probl\`emes invariants conformes et les equations de {Schr\"odinger} \`a potentiels antisymetriques}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {9}, pages = {1--14}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2006}, doi = {10.5802/jedp.36}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/jedp.36/} }
TY - JOUR AU - Rivière, Tristan TI - Lois de conservation pour les problèmes invariants conformes et les equations de Schrödinger à potentiels antisymetriques JO - Journées équations aux dérivées partielles PY - 2006 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.36/ DO - 10.5802/jedp.36 LA - fr ID - JEDP_2006____A9_0 ER -
%0 Journal Article %A Rivière, Tristan %T Lois de conservation pour les problèmes invariants conformes et les equations de Schrödinger à potentiels antisymetriques %J Journées équations aux dérivées partielles %D 2006 %P 1-14 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.36/ %R 10.5802/jedp.36 %G fr %F JEDP_2006____A9_0
Rivière, Tristan. Lois de conservation pour les problèmes invariants conformes et les equations de Schrödinger à potentiels antisymetriques. Journées équations aux dérivées partielles (2006), article no. 9, 14 p. doi : 10.5802/jedp.36. http://www.numdam.org/articles/10.5802/jedp.36/
[Bet1] Bethuel, Fabrice « Un résultat de régularité pour les solutions de l’équation de surfaces à courbure moyenne prescrite ». (French) [A regularity result for solutions to the equation of surfaces of prescribed mean curvature] C. R. Acad. Sci. Paris Sér. I Math. 314 (1992), no. 13, 1003–1007. | Zbl
[BeG1] Bethuel, F. ; Ghidaglia, J.-M. Improved regularity of solutions to elliptic equations involving Jacobians and applications. J. Math. Pures Appl. (9) 72 (1993), no. 5, 441–474. | MR | Zbl
[BeG2] Bethuel, Fabrice ; Ghidaglia, Jean-Michel « Some applications of the coarea formula to partial differential equations ». Geometry in partial differential equations, 1–17, World Sci. Publishing, River Edge, NJ, 1994. | MR | Zbl
[BrC] Brézis, Haim ; Coron, Jean-Michel « Multiple solutions of -systems and Rellich’s conjecture ». Comm. Pure Appl. Math. 37 (1984), no. 2, 149–187. | Zbl
[CLMS] Coifman, R. ; Lions, P.-L. ; Meyer, Y. ; Semmes, S. « Compensated compactness and Hardy spaces ». J. Math. Pures Appl. (9) 72 (1993), no. 3, 247–286. | MR | Zbl
[Ev] Evans Craig « Partial regularity for stationary harmonic maps into spheres » Arch. Rat. Mech. Anal. 116 (1991), 101-113. | MR | Zbl
[Fre] Frehse, Jens « A discontinuous solution of a midly nonlinear elliptic system ». Math. Z. 134 (1973), 229-230. | MR | Zbl
[FMS] Freire Alexandre, Müller Stefan and Struwe Michael « Weak compactness of wave maps and harmonic maps » Ann. Inst. Henri Poincaré 15 (1998), no. 6, 725-754. | Numdam | MR | Zbl
[Gr1] Grüter, Michael “Conformally invariant variational integrals and the removability of isolated singularities.” Manuscripta Math. 47 (1984), no. 1-3, 85–104. | Zbl
[Gr2] Grüter, Michael “Regularity of weak -surfaces”. J. Reine Angew. Math. 329 (1981), 1–15. | Zbl
[HiW] Hildebrandt, Stefan ; Widman, Kjell-Ove « Some regularity results for quasilinear elliptic systems of second order. » Math. Z. 142 (1975), 67–86. | MR | Zbl
[Hei1] Heinz, Erhard « Ein Regularitätssatz für schwache Lösungen nichtlinearer elliptischer Systeme ». (German) Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1975, no. 1, 1–13. | MR | Zbl
[Hei2] Heinz, Erhard "Über die Regularität der Lösungen nichtlinearer Wellengleichungen". (German) Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1975, no. 2, 15–26 | MR | Zbl
[Hei3] Heinz, Erhard "Über die Regularität schwacher Lösungen nichtlinearer elliptischer Systeme". (German) [On the regularity of weak solutions of nonlinear elliptic systems] Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1986, no. 1, 1–15. | MR | Zbl
[Hel] Hélein, Frédéric « Harmonic maps, conservation laws and moving frames ». Cambridge Tracts in Mathematics, 150. Cambridge University Press, Cambridge, 2002. | MR | Zbl
[Hil] Hildebrandt, S. « Nonlinear elliptic systems and harmonic mappings. » Proceedings of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, vol 1,2,3 (Beijing, 1980), 481-615, Science Press, Beijing, 1982. | MR | Zbl
[Hil2] Hildebrandt, S. « Quasilinear elliptic systems in diagonal form ». Systems of nonlinear partial differential equations (Oxford, 1982), 173-217, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 111, Reidel, Dordrecht, 1983. | MR | Zbl
[JoK] Jost, J ; Karcher, H « Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen » Manuscripta Math. 40 (1982), 27-77.x | MR | Zbl
[Kp] Kilpeläinen, T « Homogeneous and conformally invariant variational integrals » Ann. Acad. Sci. Fenn. A, I. Mat. Diss. 57, (1985). | MR | Zbl
[LaU] Ladyzhenskaya, Olga A. ; Ural’tseva, Nina N. « Linear and quasilinear elliptic equations ». Academic Press, New York-London 1968.
[LaR] Lamm, Tobias ; Rivière, Tristan « Conservation laws for fourth order systems in four dimensions » preprint (2006).
[LiR] Lin, Fang-Hua ; Rivière, Tristan « Energy quantization for harmonic maps ». Duke Math. J. 111 (2002), no. 1, 177–193. | MR | Zbl
[Mo] Morrey, Charles B., Jr. « Multiple integrals in the calculus of variations ». Die Grundlehren der mathematischen Wissenschaften, Band 130 Springer-Verlag New York, Inc., New York 1966 | MR | Zbl
[Mu] Müller, Stefan « Higher integrability of determinants and weak convergence in ». J. Reine Angew. Math. 412 (1990), 20–34. | MR | Zbl
[Ri1] Rivière, Tristan « Conservation laws for conformally invariant variational problems » preprint (2006).
[Sc1] Schoen, Richard « Analytic aspects of the harmonic map problem » Math. Sci. Res. Inst. Publ. 2 (Seminar on nonlinear partial differential equations, Berkeley, CA, 1983), ed. S.S.Chern, Springer, New-York, 1984, 321-358. | MR | Zbl
[Sha] Shatah, Jalal Weak solutions and development of singularities of the -model. Comm. Pure Appl. Math. 41 (1988), no. 4, 459–469. | MR | Zbl
[StR] Struwe, Michael ; Rivière Tristan « Partial regularity for Harmonic Maps revisited » preprint (2006).
[Ta1] Tartar, Luc « Remarks on oscillations and Stokes’ equation. Macroscopic modelling of turbulent flows » (Nice, 1984), 24–31, Lecture Notes in Phys., 230, Springer, Berlin, 1985 | Zbl
[Uhl] Uhlenbeck, Karen K. “Connections with bounds on curvature.” Comm. Math. Phys. 83 (1982), no. 1, 31–42. | Zbl
[We] Wente, Henry C. « An existence theorem for surfaces of constant mean curvature ». J. Math. Anal. Appl. 26 1969 318–344. | MR | Zbl
Cited by Sources: