A nonlocal singular perturbation problem with periodic well potential
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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 $\Gamma$-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 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
Keywords: gamma-convergence, nonlocal variational problem, micromagnetism
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Kurzke, Matthias. A nonlocal singular perturbation problem with periodic well potential. ESAIM: Control, Optimisation and Calculus of Variations, Volume 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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