A nonlocal singular perturbation problem with periodic well potential
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 52-63.

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 L p 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.

DOI : 10.1051/cocv:2005037
Classification : 49J45
Mots-clés : gamma-convergence, nonlocal variational problem, micromagnetism 
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     title = {A nonlocal singular perturbation problem with periodic well potential},
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     pages = {52--63},
     publisher = {EDP-Sciences},
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Kurzke, Matthias. A nonlocal singular perturbation problem with periodic well potential. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 52-63. doi : 10.1051/cocv:2005037. http://archive.numdam.org/articles/10.1051/cocv:2005037/

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