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Zeitschrift für Analysis und ihre Anwendungen

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Volume 19, Issue 2, 2000, pp. 415–428
DOI: 10.4171/ZAA/959

Published online: 2000-06-30

Weierstrass-Type Maximum Principle for Microstructure in Micromagnetics

Martin Kružík[1] and Tomáš Roubíček[2]

(1) Czech Technical University, Prague, Czech Republic
(2) Charles University, Praha, Czech Republic

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.

Keywords: Calculus of variations, convexification, ferromagnetism, micromagnetics, optimality conditions, relaxation, Young measures

Kružík Martin, Roubíček Tomáš: Weierstrass-Type Maximum Principle for Microstructure in Micromagnetics. Z. Anal. Anwend. 19 (2000), 415-428. doi: 10.4171/ZAA/959