A nonlocal singular perturbation problem with periodic well potential
ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 1, p. 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 : https://doi.org/10.1051/cocv:2005037
Classification:  49J45
Keywords: gamma-convergence, nonlocal variational problem, micromagnetism
@article{COCV_2006__12_1_52_0,
author = {Kurzke, Matthias},
title = {A nonlocal singular perturbation problem with periodic well potential},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {12},
number = {1},
year = {2006},
pages = {52-63},
doi = {10.1051/cocv:2005037},
zbl = {1107.49016},
mrnumber = {2192068},
language = {en},
url = {http://www.numdam.org/item/COCV_2006__12_1_52_0}
}

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://www.numdam.org/item/COCV_2006__12_1_52_0/

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