A nonlocal singular perturbation problem with periodic well potential

Issue		ESAIM: COCV Volume 12, Number 1, January 2006


Page(s)		52 - 63
DOI		10.1051/cocv:2005037
Published online		15 December 2005

ESAIM: COCV, January 2006, Vol. 12, pp. 52-63
DOI: 10.1051/cocv:2005037

A nonlocal singular perturbation problem with periodic well potential

Matthias Kurzke

Institute for Mathematics and its Applications, University of Minnesota, 400 Lind Hall, 207 Church Street SE, Minneapolis, MN 55455, USA; kurzke@ima.umn.edu

(Received September 2, 2004. Accepted January 4, 2005. / Published online: 15 December 2005)

Abstract
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.

Mathematics Subject Classification. 49J45

Key words: Gamma-convergence, nonlocal variational problem, micromagnetism

© EDP Sciences, SMAI 2006

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