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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