Weierstrass-Type Maximum Principle for Microstructure in Micromagnetics

Abstract

We derive necessary and sufficient optimality conditions for a relaxed (in terms of Young measures) variational problem governing steady states of ferromagnetic materials. Such conditions here stated in the form of a generalized Weierstrass maximum principle enable us to establish uniqueness of a solution in some specific situations and can also be used in efficient numerical algorithms solving the relaxed problems, for instance.