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A nonlocal singular perturbation problem with periodic well potential. (English) Zbl 1107.49016

Summary: For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a \(\Gamma\)-convergence theorem and show compactness up to translation in all \(L^p\) and the optimal Orlicz space for sequences of bounded energy. This generalizes work of G. Alberti, G. Bouchitté and P. Seppecher [C. R. Acad. Sci., Paris, Sér. I 319, No. 4, 333–338 (1994; Zbl 0845.49008)] for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.

MSC:

49J45 Methods involving semicontinuity and convergence; relaxation
82D40 Statistical mechanics of magnetic materials

Citations:

Zbl 0845.49008
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References:

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