Volume 12, Number 1, January 2006
|Page(s)||52 - 63|
|Published online||15 December 2005|
A nonlocal singular perturbation problem with periodic well potential
Institute for Mathematics and its Applications,
University of Minnesota,
400 Lind Hall,
207 Church Street SE,
Minneapolis, MN 55455,
Accepted: 4 January 2005
For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a Γ-convergence theorem and show compactness up to translation in all Lp and the optimal Orlicz space for sequences of bounded energy. 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 of the micromagnetic energy.
Mathematics Subject Classification: 49J45
Key words: Gamma-convergence / nonlocal variational problem / micromagnetism
© EDP Sciences, SMAI, 2006
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