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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 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.
@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},
pages = {52--63},
publisher = {EDP-Sciences},
volume = {12},
number = {1},
year = {2006},
doi = {10.1051/cocv:2005037},
mrnumber = {2192068},
zbl = {1107.49016},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005037/}
}
TY - JOUR AU - Kurzke, Matthias TI - A nonlocal singular perturbation problem with periodic well potential JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 52 EP - 63 VL - 12 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005037/ DO - 10.1051/cocv:2005037 LA - en ID - COCV_2006__12_1_52_0 ER -
%0 Journal Article %A Kurzke, Matthias %T A nonlocal singular perturbation problem with periodic well potential %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 52-63 %V 12 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005037/ %R 10.1051/cocv:2005037 %G en %F COCV_2006__12_1_52_0
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
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