MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Weierstrass-type maximum principle for microstructure in micromagnetics

Martin Kruzik and Tomas Roubicek


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.

MSC Codes:
49K20, 49K35, 49S05
calculus of variation, convexification, ferromagnetism, micromagnetics, optimality conditions, relaxation, young measure

Related publications

2000 Repository Open Access
Martin Kružík and Tomas Roubicek

Weierstrass-type maximum principle for microstructure in micromagnetics

In: Zeitschrift fuer Analysis und ihre Anwendungen, 19 (2000) 2, pp. 415-428