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.
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Martin Kružík, Tomáš Roubíček, Weierstrass-Type Maximum Principle for Microstructure in Micromagnetics. Z. Anal. Anwend. 19 (2000), no. 2, pp. 415–428DOI 10.4171/ZAA/959