3D-2D asymptotic analysis for micromagnetic thin films

Gamma -convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness epsil on approaches zero of a ferromagnetic thin structure Omega (epsilon) = omeg a x (epsilon,epsilon), omega subset of R-2, whose energy is given by epsilon (epsilon)((m) over bar) = 1/epsilon integral (Omega epsilon) (W((m) over bar,del(m) over bar) + 1/2 del(u) over bar . (m) over bar) dx subject to div(-del(u) over bar + (m) over bar chi Omega (epsilon)) = 0 on R-3, and to the constraint \(m) over bar\ = 1 on Omega (epsilon), where W is any continuous function satisfying p-growth assumptions with p > 1. Partial results are also obtained in the case p = 1, under an additional assumption on W.