Weierstrass-type maximum principle for microstructure in micromagnetics
Martin Kruzik and Tomas Roubicek
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Submission date: 31. May. 1999
published in: Zeitschrift fuer Analysis und ihre Anwendungen, 19 (2000) 2, p. 415-428
MSC-Numbers: 49K20, 49K35, 49S05
Keywords and phrases: calculus of variation, convexification, ferromagnetism, micromagnetics, optimality conditions, relaxation, young measure
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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.