Energy concentration for the Landau–Lifshitz equation

Roger Moser

Annales de l'I.H.P. Analyse non linéaire (2008)

  • Volume: 25, Issue: 5, page 987-1013
  • ISSN: 0294-1449

How to cite

top

Moser, Roger. "Energy concentration for the Landau–Lifshitz equation." Annales de l'I.H.P. Analyse non linéaire 25.5 (2008): 987-1013. <http://eudml.org/doc/78822>.

@article{Moser2008,
author = {Moser, Roger},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Landau-Lifshitz equation; energy concentration; mean curvature flow},
language = {eng},
number = {5},
pages = {987-1013},
publisher = {Elsevier},
title = {Energy concentration for the Landau–Lifshitz equation},
url = {http://eudml.org/doc/78822},
volume = {25},
year = {2008},
}

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
PB - Elsevier
VL - 25
IS - 5
SP - 987
EP - 1013
LA - eng
KW - Landau-Lifshitz equation; energy concentration; mean curvature flow
UR - http://eudml.org/doc/78822
ER -

References

top
  1. [1] Allard W.K., On the first variation of a varifold, Ann. of Math. (2)95 (1972) 417-491. Zbl0252.49028MR307015
  2. [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. Zbl1043.35136MR1655508
  3. [3] Brakke K.A., The Motion of a Surface by its Mean Curvature, Mathematical Notes, vol. 20, Princeton University Press, Princeton, NJ, 1978. Zbl0386.53047MR485012
  4. [4] Coifman R., Lions P.L., Meyer Y., Semmes S., Compensated compactness and Hardy spaces, J. Math. Pures Appl.72 (1993) 247-286. Zbl0864.42009MR1225511
  5. [5] Ding W., Tian G., Energy identity for a class of approximate harmonic maps from surfaces, Comm. Anal. Geom.3 (1995) 543-554. Zbl0855.58016MR1371209
  6. [6] Eells J., Lemaire L., A report on harmonic maps, Bull. London Math. Soc.10 (1978) 1-68. Zbl0401.58003MR495450
  7. [7] Federer H., Geometric Measure Theory, Springer-Verlag, New York, 1969. Zbl0176.00801MR257325
  8. [8] Feldman M., Partial regularity for harmonic maps of evolution into spheres, Comm. Partial Differential Equations19 (1994) 761-790. Zbl0807.35021MR1274539
  9. [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. Zbl0728.35014MR1078114
  10. [10] Hutchinson J.E., Second fundamental form for varifolds and the existence of surfaces minimising curvature, Indiana Univ. Math. J.35 (1986) 45-71. Zbl0561.53008MR825628
  11. [11] Jost J., Two-Dimensional Geometric Variational Problems, John Wiley & Sons, Chichester, 1991. Zbl0729.49001MR1100926
  12. [12] Li J., Tian G., The blow-up locus of heat flows for harmonic maps, Acta Math. Sin. (Engl. Ser.)16 (2000) 29-62. Zbl0959.58021MR1760521
  13. [13] Lin F.-H., Gradient estimates and blow-up analysis for stationary harmonic maps, Ann. of Math. (2)149 (1999) 785-829. Zbl0949.58017MR1709303
  14. [14] Lin F.-H., Mapping problems, fundamental groups and defect measures, Acta Math. Sin. (Engl. Ser.)15 (1999) 25-52. Zbl0926.49025MR1701132
  15. [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. Zbl1056.58007MR1830199
  16. [16] Lin F.-H., Rivière T., Energy quantization for harmonic maps, Duke Math. J.111 (2002) 177-193. Zbl1014.58008MR1876445
  17. [17] Lin F.-H., Wang C., Energy identity of harmonic map flows from surfaces at finite singular time, Calc. Var. Partial Differential Equations6 (1998) 369-380. Zbl0908.58008MR1624304
  18. [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 Linéaire19 (2002) 209-259. Zbl1042.58006MR1902744
  19. [19] Moser R., Energy concentration for almost harmonic maps and the Willmore functional, Math. Z.251 (2005) 293-311. Zbl1079.58013MR2191029
  20. [20] Moser R., Partial Regularity for Harmonic Maps and Related Problems, World Scientific Publishing Co. Pte. Ltd, Singapore, 2005. Zbl1246.58012MR2155901
  21. [21] Qing J., On singularities of the heat flow for harmonic maps from surfaces into spheres, Comm. Anal. Geom.3 (1995) 297-315. Zbl0868.58021MR1362654
  22. [22] Qing J., Tian G., Bubbling of the heat flows for harmonic maps from surfaces, Comm. Pure Appl. Math.50 (1997) 295-310. Zbl0879.58017MR1438148
  23. [23] Sacks J., Uhlenbeck K., The existence of minimal immersions of 2-spheres, Ann. of Math. (2)113 (1981) 1-24. Zbl0462.58014MR604040
  24. [24] Simon L., Lectures on Geometric Measure Theory, Australian National University Centre for Mathematical Analysis, Canberra, 1983. Zbl0546.49019MR756417
  25. [25] Stein E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ, 1993. Zbl0821.42001MR1232192
  26. [26] Struwe M., On the evolution of harmonic maps in higher dimensions, J. Differential Geom.28 (1988) 485-502. Zbl0631.58004MR965226
  27. [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. Zbl0929.46028MR1662313
  28. [28] Willmore T.J., Riemannian Geometry, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993. Zbl0797.53002MR1261641

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.