3D-2D Asymptotic Analysis for Micromagnetic Thin Films

DOI10.1051/cocv:2001119zbMath0989.35009OpenAlexW2088521483MaRDI QIDQ4331447

Roberto Alicandro, Chiara Leone

Publication date: 16 May 2002

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=COCV_2001__6__489_0

zbMATH Keywords

Gamma-limitrelaxation of constrained functionals

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Thin films (74K35) PDEs of mixed type (35M10) Methods involving semicontinuity and convergence; relaxation (49J45)

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Homogenization of variational problems in manifold valued \(BV\)-spaces ⋮ A note on the 3D–2D dimensional reduction of a micromagnetic thin film with nonhomogeneous profile ⋮ Junction of ferromagnetic thin films ⋮ Junction of quasi-stationary ferromagnetic wires ⋮ A reduced model for the polarization in a ferroelectric thin wire ⋮ Asymptotic analysis for two joined thin slanting ferromagnetic films ⋮ Relaxation of nonlinear elastic energies involving the deformed configuration and applications to nematic elastomers ⋮ Thin film limits in magnetoelastic interactions ⋮ Ferromagnetic thin multi-structures ⋮ Quasy-stationary ferromagnetic thin films in degenerated cases ⋮ MODELING THIN CURVED FERROMAGNETIC FILMS ⋮ Curved ferromagnetic thin films ⋮ Homogenization of variational problems in manifold valued Sobolev spaces ⋮ Fin junction of ferroelectric thin films ⋮ Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings

Cites Work

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• An introduction to \(\Gamma\)-convergence
• On the inadequacy of the scaling of linear elasticity for 3D-2D asymptotics in a nonlinear setting
• Manifold constrained variational problems
• Quasi-convexity and the lower semicontinuity of multiple integrals
• 3D-2D Asymptotic Analysis for Inhomogeneous Thin Films
• Quasi-Convex Integrands and Lower Semicontinuity in $L^1 $
• 3D-2D asymptotic analysis of an optimal design problem for thin films
• Direct methods in the calculus of variations
• Brittle thin films

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