Homogenization of micromagnetics large bodies
ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 295-314.

A homogenization problem related to the micromagnetic energy functional is studied. In particular, the existence of the integral representation for the homogenized limit of a family of energies

ε (m)= Ω φx,x ε,m(x)dx- Ω h e (x)·m(x)dx+1 2 3 |u(x)| 2 dx
of a large ferromagnetic body is obtained.

DOI : 10.1051/cocv:2004008
Classification : 35B27, 74Q99, 82D40
Mots clés : micromagnetics, homogenization, $\Gamma $-convergence
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     title = {Homogenization of micromagnetics large bodies},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {295--314},
     publisher = {EDP-Sciences},
     volume = {10},
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Pisante, Giovanni. Homogenization of micromagnetics large bodies. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 2, pp. 295-314. doi : 10.1051/cocv:2004008. http://www.numdam.org/articles/10.1051/cocv:2004008/

[1] G. Anzellotti, S. Baldo and A. Visintin, Asymptotic behavior of the Landau-Lifshitz model of ferromagnetism. Appl. Math. Optim. 23 (1991) 171-192. | MR | Zbl

[2] J.M. Ball, A. Taheri and M. Winter, Local minimizers in micromagnetics and related problems. Calc. Var. Partial Differ. Equ. 14 (2002) 1-27. | MR | Zbl

[3] A. Braides and A. Defranceschi, Homogenization of multiple integrals. The Clarendon Press Oxford University Press, New York, Oxford Lecture Ser. Math. Appl. 12 (1998). | MR | Zbl

[4] A. Braides, I. Fonseca and G. Leoni, A-quasiconvexity: relaxation and homogenization. ESAIM: COCV 5 (2000) 539-577 (electronic). | Numdam | MR | Zbl

[5] Jr. Brown and W. Fuller, Micromagnetics. Interscience Publishers, John Wiley & Sons, New York, London (1963).

[6] B. Dacorogna, Direct methods in the calculus of variations. Appl. Math. Sci. 78 (1989). | MR | Zbl

[7] B. Dacorogna and I. Fonseca, A-B quasiconvexity and implicit partial differential equations. Calc. Var. Partial Differ. Equ. 14 (2002) 115-149. | MR | Zbl

[8] G. Dal Maso, An introduction to Γ-convergence. Birkhäuser Boston Inc., Boston, MA Prog. Nonlinear Differ. Equ. Appl. 8 (1993). | MR | Zbl

[9] A. De Simone, Energy minimizers for large ferromagnetic bodies. Arch. Ration. Mech. Anal. 125 (1993) 99-143. | MR | Zbl

[10] A. De Simone, Hysteresis and imperfection sensitivity in small ferromagnetic particles. Meccanica 30 (1995) 591-603. Microstructure and phase transitions in solids (Udine, 1994). | MR | Zbl

[11] A. De simone, R.V. Kohn, S. Müller and F. Otto, A reduced theory for thin-film micromagnetics. Commun. Pure Appl. Math. 55 (2002) 1408-1460. | MR | Zbl

[12] A. De Simone, S. Müller, R.V. Kohn and F. Otto, A compactness result in the gradient theory of phase transitions. Proc. R. Soc. Edinb. Sect. A 131 (2001) 833-844. | MR | Zbl

[13] I. Fonseca and G. Leoni, Relaxation results in micromagnetics. Ricerche Mat. 49 (2000) (suppl.) 269-304. Contributions in honor of the memory of Ennio De Giorgi (Italian). | MR | Zbl

[14] R.D. James and D. Kinderlehrer, Frustration in ferromagnetic materials. Contin. Mech. Thermodyn. 2 (1990) 215-239. | MR

[15] L.D. Landau and E.M. Lifshits, Teoreticheskaya fizika. Tome VIII. “Nauka”, Moscow, third edition (1992). Elektrodinamika sploshnykh sred. [Electrodynamics of continuous media], with a preface by Lifshits and L.P. Pitaevskiĭ, edited and with a preface by Pitaevskiĭ.

[16] L. Tartar, On mathematical tools for studying partial differential equations of continuum physics: H-measures and Young measures. Plenum, New York, in Developments in partial differential equations and applications to mathematical physics (Ferrara, 1991), (1992) 201-217. | MR | Zbl

[17] L. Tartar, Beyond Young measures. Meccanica 30 (1995) 505-526. Microstructure and phase transitions in solids (Udine, 1994). | MR | Zbl

[18] A. Visintin, On Landau-Lifshitz' equations for ferromagnetism. Japan J. Appl. Math. 2 (1985) 69-84. | Zbl

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