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We study the existence of minimizers for 2-dimensional ferromagnetism with various assumptions on different terms of the total energy. Our general philosophy for finding the minimizing magnetizations is to reduce this problem to a minimization problem for a new energy over a divergence-free field. Such a general philosophy works for all dimensions. However,(More)
We introduce multi-scale Young measures to deal with problems where multi-scale phenomena are relevant. We prove some interesting representation results that allow the use of these families of measures in practice, and illustrate its applicability by treating, from this perspective, multi-scale convergence and homogenization of multiple integrals.
We analyze a typical 3-D conductivity problem which consists in seeking the optimal layout of two materials in a given design domain Ω ⊂ IR 3 by minimizing the L 2-norm of the electric field under a constraint on the amount on each material that we can use. We utilize a characterization of the three-dimensional divergence-free vector fields which is(More)
We present a new method for micromagnetics based on replacing the nonlocal total energy of magnetizations by a new local energy for divergence-free fields and then studying the dual Legendre functional of this new energy restricted on gradient fields. We establish a Fenchel-type duality principle relevant to the minimization for these problems. The dual(More)
We analyze in this work a spatio-temporal optimal design problem governed by a linear damped 1-D wave equation. The problem consists in seeking simultaneously the spatio-temporal layout of two isotropic materials and the static position of the damping set in order to minimize a functional depending quadratically on the gradient of the state. The lack of(More)