Asymptotic study of a family of energy-functionals related to micromagnetics

In a joint work with Tristan Riviere, we have studied a family of energy-functionals related to micromagnetics, in dimension 2, containing an "exchange-energy" term and a "demagnetizing-energy" term, when the constant in front of the exchange-energy tends to 0. We showed a compactness result for families of uniformly bounded energy. Such configurations converge to unit-valued divergence-free vector fields that are tangent to the boundary of the domain (such configurations have typically line singularities), and we extract a limiting energy (sort of Gamma-limit) which penalizes the jumps of the limiting configuration. We also give a kinetic formulation of the problem which allows to get an entropy-type condition for almost-minimizing families.