-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness approaches zero of a ferromagnetic thin structure , , whose energy is given by
Mots clés : $\Gamma $-limit, thin films, micromagnetics, relaxation of constrained functionals
@article{COCV_2001__6__489_0, author = {Alicandro, Roberto and Leone, Chiara}, title = {3D-2D asymptotic analysis for micromagnetic thin films}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {489--498}, publisher = {EDP-Sciences}, volume = {6}, year = {2001}, mrnumber = {1836053}, zbl = {0989.35009}, language = {en}, url = {http://www.numdam.org/item/COCV_2001__6__489_0/} }
TY - JOUR AU - Alicandro, Roberto AU - Leone, Chiara TI - 3D-2D asymptotic analysis for micromagnetic thin films JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2001 SP - 489 EP - 498 VL - 6 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_2001__6__489_0/ LA - en ID - COCV_2001__6__489_0 ER -
Alicandro, Roberto; Leone, Chiara. 3D-2D asymptotic analysis for micromagnetic thin films. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 489-498. http://www.numdam.org/item/COCV_2001__6__489_0/
[1] Homogenization of Multiple Integrals. Oxford University Press, Oxford (1998). | MR | Zbl
and ,[2] Brittle thin films, Preprint CNA-CMU. Pittsburgh (1999). | MR | Zbl
and , , and , 3D-2D asymptotic analysis for inhomogeneous thin films, Preprint CNA-CMU. Pittsburgh (1999). |[4] Micromagnetics. John Wiley and Sons, New York (1963).
,[5] Convex analysis and measurable multifunctions. Springer-Verlag, New York, Lecture Notes in Math. 580 (1977). | MR | Zbl
and ,[6] Direct methods in Calculus of Variations. Springer-Verlag, Berlin (1989). | MR | Zbl
,[7] Manifold constrained variational problems. Calc. Var. 9 (1999) 185-206. | MR | Zbl
, , and ,[8] An Introduction to -convergence. Birkhäuser, Boston (1993). | MR | Zbl
, and , 3D-2D asymptotic analysis of an optimal design problem for thin films. J. Reine Angew. Math. 505 (1998) 173-202. |[10] On the inadequacy of the scaling of linear elasticity for 3D-2D asymptotic in a nonlinear setting, Preprint CNA-CMU. Pittsburgh (1999). | MR | Zbl
and ,[11] Quasi-convex integrands and lower semicontinuity in . SIAM J. Math. Anal. 23 (1992) 1081-1098. | MR | Zbl
and ,[12] Micromagnetics of very thin films. Proc. Roy. Soc. Lond. Ser. A 453 (1997) 213-223.
and ,[13] Quasiconvexity and the semicontinuity of multiple integrals. Pacific J. Math. 2 (1952) 25-53. | MR | Zbl
,[14] Multiple integrals in the Calculus of Variations. Springer-Verlag, Berlin (1966). | MR | Zbl
,