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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
106/2003

A nonlocal singular perturbation problem with periodic well potential

Matthias Kurzke

Abstract

For a one-dimensional nonlocal nonconvex singular perturbation problem with a noncoercive periodic well potential, we prove a $\Gamma$-convergence theorem and show compactness up to translation in all $L^p$ and certain Orlicz spaces for sequences of bounded energy. This generalizes work of Alberti, Bouchitté and Seppecher for the coercive two-well case. The theorem has applications to a certain thin-film limit of the micromagnetic energy.

Received:
09.12.03
Published:
09.12.03
MSC Codes:
49J45
Keywords:
gamma-convergence, nonlocal functionals

Related publications

inJournal
2006 Repository Open Access
Matthias Kurzke

A nonlocal singular perturbation problem with periodic well potential

In: Control, optimisation and calculus of variations (ESAIM-COCV), 12 (2006) 1, pp. 52-63