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Homogenization of ferromagnetic multilayers in the presence of surface energies

Kévin Santugini-Repiquet (2007)

ESAIM: Control, Optimisation and Calculus of Variations

We study the homogenization process of ferromagnetic multilayers in the presence of surface energies: super-exchange, also called interlayer exchange coupling, and surface anisotropy. The two main difficulties are the non-linearity of the Landau-Lifshitz equation and the absence of a good sequence of extension operators for the multilayer geometry. First, we consider the case when surface anisotropy is the dominant term, then the case when the magnitude of the super-exchange interaction is...

Hysteresis filtering in the space of bounded measurable functions

Pavel Krejčí, Philippe Laurençot (2002)

Bollettino dell'Unione Matematica Italiana

We define a mapping which with each function u L 0 , T and an admissible value of r > 0 associates the function ξ with a prescribed initial condition ξ 0 which minimizes the total variation in the r -neighborhood of u in each subinterval 0 , t of 0 , T . We show that this mapping is non-expansive with respect to u , r and ξ 0 , and coincides with the so-called play operator if u is a regulated function.

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