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A nonlocal singular perturbation problem with periodic well potential

Published online by Cambridge University Press:  15 December 2005

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

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 Lp 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.

Keywords

Gamma-convergencenonlocal variational problemmicromagnetism
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 1 , January 2006 , pp. 52 - 63
Copyright
© EDP Sciences, SMAI, 2006

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References

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