Abstract :

We carry our previous study on the asymptotics of a family of energy-functionals related to micromagnetics. We prove compactness for families of uniformly bounded energies releasing the LBP condition we had previously set. Such families converge to unit-valued divergence-free vector-fields that are tangent to the boundary of the domain, and we found in that the energy-functionals Gamma-converge to a limiting jump-energy of such configurations. We examine the behavior of certain truncated fields which serve to construct ``entropies''. We give a kinetic formulation of the problem, and show that the limiting divergence-free problem is supplemented, in the case of minimizers, with a sign condition which can in turn, using the kinetic formulation, be interpreted as an entropy condition that should play a role in uniqueness questions.