# A nonlocal singular perturbation problem with periodic well potential

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- Volume: 12, Issue: 1, page 52-63
- ISSN: 1292-8119

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topKurzke, Matthias. "A nonlocal singular perturbation problem with periodic well potential." ESAIM: Control, Optimisation and Calculus of Variations 12.1 (2005): 52-63. <http://eudml.org/doc/90790>.

@article{Kurzke2005,

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.
},

author = {Kurzke, Matthias},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Gamma-convergence; nonlocal variational problem; micromagnetism},

language = {eng},

month = {12},

number = {1},

pages = {52-63},

publisher = {EDP Sciences},

title = {A nonlocal singular perturbation problem with periodic well potential},

url = {http://eudml.org/doc/90790},

volume = {12},

year = {2005},

}

TY - JOUR

AU - Kurzke, Matthias

TI - A nonlocal singular perturbation problem with periodic well potential

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2005/12//

PB - EDP Sciences

VL - 12

IS - 1

SP - 52

EP - 63

AB -
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.

LA - eng

KW - Gamma-convergence; nonlocal variational problem; micromagnetism

UR - http://eudml.org/doc/90790

ER -

## References

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- P. Pedregal, Parametrized measures and variational principles, Progre. Nonlinear Differ. Equ. Appl.30 (1997).
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