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For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a -convergence theorem and show compactness up to translation in all 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.
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.
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