Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter May 8, 2014

Concentration compactness of a Landau-Lifschitz type energy with radial structure

  • Bei Wang EMAIL logo , Yuze Cai and Yutian Lei
From the journal Mathematica Slovaca


This paper is concerned with the asymptotic behavior of a p-Landau-Lifschitz type functional with radial structure as parameter goes to zero. We study the concentration compactness properties in the case of p ≥ n where n is the dimension. By analyzing the functional globally, we show that the singularity of p-Landau-Lifschitz energy concentrates on the origin.

[1] ALMOG, Y.— BERLYAND, L.— GOLOVATY, D.— SHAFRIR, I.: Global minimizers for a p-Ginzburg-Landau-type energy in R 2, J. Funct. Anal. 256 (2009), 2268–2290. in Google Scholar

[2] BETHUEL, F.— BREZIS, H.— HELEIN, F.: Ginzburg-Landau Vortices, Birkhauser, Boston, 1994. in Google Scholar

[3] HAN, Z.— LI, Y.: Degenerate elliptic systems and applications to Ginzburg-Landau type equations, Part I, Calc. Var. Partial Differential Equations 4 (1996), 171–202. in Google Scholar

[4] HANG, F.— LIN, F.: Static theory for Planar Ferromagnets and Antiferromagnets, Acta. Math. Sinica 17 (2001), 541–580. in Google Scholar

[5] HONG, M.: Asymptotic behavior for minimizers of a Ginzburg-Landau type functional in higher dimensions associated with n-harmonic maps, Adv. Differential Equations 1 (1996), 611–634. 10.57262/ade/1366896030Search in Google Scholar

[6] KOMINEAS, S.— PAPANICOLAOU, N.: Vortex dynamics in two-dimensional antiferromagnets, Nonlinearity 11 (1998), 265–290. in Google Scholar

[7] LEI, Y.: Asymptotic analysis of the radial minimizers of an energy functional, Methods Appl. Anal. 10 (2003), 67–80. 10.4310/MAA.2003.v10.n1.a4Search in Google Scholar

[8] LEI, Y.: Asymptotic properties of minimizers of a p-energy functional, Nonlinear Anal. 68 (2008), 1421–1431. in Google Scholar

[9] LEI, Y.: Some results on an n-Ginzburg-Landau type minimizer, J. Comput. Appl. Math. 217 (2008), 123–136. in Google Scholar

[10] LEI, Y.: Singularity analysis of a p-Ginzburg-Landau type minimizer, Bull. Sci. Math. 134 (2010), 97–115. in Google Scholar

[11] MOSER, R.: Ginzburg-Landau vortices for thin ferromagnetic films, Appl. Math. Res. Express. AMRX (2003), 1–32. Search in Google Scholar

[12] PAPANICOLAOU, N.— SPATHIS, P. N.: Semitopological solutions in planar ferromagnets, Nonlinearity 12 (1999), 285–302. in Google Scholar

[13] QI, L.— LEI, Y.: On energy estimates for a Landau-Lifschitz type functional in higher dimensions, J. Korean Math. Soc. 46 (2009), 1207–1218. in Google Scholar

[14] SANDIER E.: Ginzburg-Landau minimizers from R n+1to R nand minimal connections, Indiana Univ. Math. J. 50 (2001), 1807–1844. in Google Scholar

[15] STRUWE, M.: Une estimation asymptotique pour le modéle Ginzburg-Landau, C. R. Math. Acad. Sci. Paris 317 (1993), 677–680. Search in Google Scholar

[16] WANG, C.: Limits of solutions to the generalized Ginzburg-Landau functional, Comm. Partial Differential Equations 27 (2002), 877–906. in Google Scholar

Published Online: 2014-5-8
Published in Print: 2014-4-1

© 2014 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Downloaded on 1.3.2024 from
Scroll to top button