Energy concentration for the Landau-Lifshitz equation

Moser, Roger

doi:10.1016/j.anihpc.2007.08.003

Moser, Roger

Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 5, pp. 987-1013

MR Zbl

DOI : 10.1016/j.anihpc.2007.08.003

@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},
     pages = {987--1013},
     year = {2008},
     publisher = {Elsevier},
     volume = {25},
     number = {5},
     doi = {10.1016/j.anihpc.2007.08.003},
     mrnumber = {2457820},
     zbl = {1158.35098},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2007.08.003/}
}

TY  - JOUR
AU  - Moser, Roger
TI  - Energy concentration for the Landau-Lifshitz equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2008
SP  - 987
EP  - 1013
VL  - 25
IS  - 5
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2007.08.003/
DO  - 10.1016/j.anihpc.2007.08.003
LA  - en
ID  - AIHPC_2008__25_5_987_0
ER  -

%0 Journal Article
%A Moser, Roger
%T Energy concentration for the Landau-Lifshitz equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2008
%P 987-1013
%V 25
%N 5
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2007.08.003/
%R 10.1016/j.anihpc.2007.08.003
%G en
%F 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) no. 5, pp. 987-1013. doi: 10.1016/j.anihpc.2007.08.003

Bibliographie
Cité par

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

[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. | Zbl | MR | Numdam

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

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

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

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

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

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

[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. | Zbl | MR

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

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

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

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR

[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. | Zbl | MR | Numdam

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

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

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

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

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

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

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

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

[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. | Zbl | MR

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

Cité par Sources :