Energy concentration for the Landau-Lifshitz equation
Moser, Roger
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 987-1013 / Harvested from Numdam
@article{AIHPC_2008__25_5_987_0,
     author = {Moser, Roger},
     title = {Energy concentration for the Landau-Lifshitz equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {987-1013},
     doi = {10.1016/j.anihpc.2007.08.003},
     mrnumber = {2457820},
     zbl = {1158.35098},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_5_987_0}
}
Moser, Roger. Energy concentration for the Landau-Lifshitz equation. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 987-1013. doi : 10.1016/j.anihpc.2007.08.003. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_5_987_0/

[1] Allard W.K., On the first variation of a varifold, Ann. of Math. (2) 95 (1972) 417-491. | MR 307015 | Zbl 0252.49028

[2] Ambrosio L., Soner H.M., A measure-theoretic approach to higher codimension mean curvature flows, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) 27-49. | Numdam | MR 1655508 | Zbl 1043.35136

[3] Brakke K.A., The Motion of a Surface by its Mean Curvature, Mathematical Notes, vol. 20, Princeton University Press, Princeton, NJ, 1978. | MR 485012 | Zbl 0386.53047

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

[5] Ding W., Tian G., Energy identity for a class of approximate harmonic maps from surfaces, Comm. Anal. Geom. 3 (1995) 543-554. | MR 1371209 | Zbl 0855.58016

[6] Eells J., Lemaire L., A report on harmonic maps, Bull. London Math. Soc. 10 (1978) 1-68. | MR 495450 | Zbl 0401.58003

[7] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. | MR 257325 | Zbl 0176.00801

[8] Feldman M., Partial regularity for harmonic maps of evolution into spheres, Comm. Partial Differential Equations 19 (1994) 761-790. | MR 1274539 | Zbl 0807.35021

[9] Hélein F., Régularité des applications faiblement harmoniques entre une surface et une sphère, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 519-524. | MR 1078114 | Zbl 0728.35014

[10] Hutchinson J.E., Second fundamental form for varifolds and the existence of surfaces minimising curvature, Indiana Univ. Math. J. 35 (1986) 45-71. | MR 825628 | Zbl 0561.53008

[11] Jost J., Two-Dimensional Geometric Variational Problems, John Wiley & Sons, Chichester, 1991. | MR 1100926 | Zbl 0729.49001

[12] Li J., Tian G., The blow-up locus of heat flows for harmonic maps, Acta Math. Sin. (Engl. Ser.) 16 (2000) 29-62. | MR 1760521 | Zbl 0959.58021

[13] Lin F.-H., Gradient estimates and blow-up analysis for stationary harmonic maps, Ann. of Math. (2) 149 (1999) 785-829. | MR 1709303 | Zbl 0949.58017

[14] Lin F.-H., Mapping problems, fundamental groups and defect measures, Acta Math. Sin. (Engl. Ser.) 15 (1999) 25-52. | MR 1701132 | Zbl 0926.49025

[15] Lin F.-H., Varifold type theory for Sobolev mappings, in: First International Congress of Chinese Mathematicians, Beijing, 1998, Amer. Math. Soc., Providence, 2001, pp. 423-430. | MR 1830199 | Zbl 1056.58007

[16] Lin F.-H., Rivière T., Energy quantization for harmonic maps, Duke Math. J. 111 (2002) 177-193. | MR 1876445 | Zbl 1014.58008

[17] Lin F.-H., Wang C., Energy identity of harmonic map flows from surfaces at finite singular time, Calc. Var. Partial Differential Equations 6 (1998) 369-380. | MR 1624304 | Zbl 0908.58008

[18] Lin F.-H., Wang C., Harmonic and quasi-harmonic spheres. III. Rectifiability of the parabolic defect measure and generalized varifold flows, Ann. Inst. H. Poincaré Anal. Non Linéaire 19 (2002) 209-259. | Numdam | MR 1902744 | Zbl 1042.58006

[19] Moser R., Energy concentration for almost harmonic maps and the Willmore functional, Math. Z. 251 (2005) 293-311. | MR 2191029 | Zbl 1079.58013

[20] Moser R., Partial Regularity for Harmonic Maps and Related Problems, World Scientific Publishing Co. Pte. Ltd, Singapore, 2005. | MR 2155901 | Zbl pre02139246

[21] Qing J., On singularities of the heat flow for harmonic maps from surfaces into spheres, Comm. Anal. Geom. 3 (1995) 297-315. | MR 1362654 | Zbl 0868.58021

[22] Qing J., Tian G., Bubbling of the heat flows for harmonic maps from surfaces, Comm. Pure Appl. Math. 50 (1997) 295-310. | MR 1438148 | Zbl 0879.58017

[23] Sacks J., Uhlenbeck K., The existence of minimal immersions of 2-spheres, Ann. of Math. (2) 113 (1981) 1-24. | MR 604040 | Zbl 0462.58014

[24] Simon L., Lectures on Geometric Measure Theory, Australian National University Centre for Mathematical Analysis, Canberra, 1983. | MR 756417 | Zbl 0546.49019

[25] Stein E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993. | MR 1232192 | Zbl 0821.42001

[26] Struwe M., On the evolution of harmonic maps in higher dimensions, J. Differential Geom. 28 (1988) 485-502. | MR 965226 | Zbl 0631.58004

[27] Tartar L., Imbedding theorems of Sobolev spaces into Lorentz spaces, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (1998) 479-500. | MR 1662313 | Zbl 0929.46028

[28] Willmore T.J., Riemannian Geometry, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. | MR 1261641 | Zbl 0797.53002