A nonlocal singular perturbation problem with periodic well potential
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Submission date: 09. Dec. 2003
published in: Control, optimisation and calculus of variations (ESAIM-COCV), 12 (2006) 1, p. 52-63
DOI number (of the published article): 10.1051/cocv:2005037
Keywords and phrases: gamma-convergence, nonlocal functionals
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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 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.