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A nonlocal singular perturbation problem with periodic well potential

Matthias Kurzke — 2006

ESAIM: Control, Optimisation and Calculus of Variations

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 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.

A nonlocal singular perturbation problem with periodic well potential

Matthias Kurzke — 2005

ESAIM: Control, Optimisation and Calculus of Variations

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.

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