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A nonlocal singular perturbation problem with periodic well potential
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 certain Orlicz spaces for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.