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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 problemwith a noncoercive periodic well potential,we prove a Γ-convergence theorem and show compactnessup to translationin all Lp and the optimal Orlicz space for sequences of boundedenergy. 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 ofthe micromagnetic energy.

Keywords

Gamma-convergencenonlocal variational problemmicromagnetism

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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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