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micromagnetism

ESAIM: Control, Optimisation and Calculus of Variations (1)

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A nonlocal singular perturbation problem with periodic well potential
Matthias Kurzke
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 12 / Issue 1 / January 2006

Published online by Cambridge University Press:

15 December 2005, pp. 52-63

Print publication:

January 2006
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For a one-dimensional nonlocal nonconvex singular perturbation problemwith a noncoercive periodic well potential,we prove a Γ-convergence theorem and show compactnessup to translationin all Lp and the optimal Orlicz space for sequences of boundedenergy. This generalizes work of Alberti, Bouchitté and Seppecher(1994) for the coercive two-well case.The theorem has applications to a certain thin-film limit ofthe micromagnetic energy.