Limiting domain wall energy for a problem related to micromagnetics

Authors
Riviere, T Serfaty, S
Citation
T. Riviere et S. Serfaty, Limiting domain wall energy for a problem related to micromagnetics, COM PA MATH, 54(3), 2001, pp. 294-338
Citations number
22
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
ISSN journal
00103640 → ACNP
Volume
54
Issue
3
Year of publication
2001
Pages
294 - 338
Database
ISI
SICI code
0010-3640(200103)54:3<294:LDWEFA>2.0.ZU;2-B
Abstract
We study the asymptotic limit of a family of functionals related to the the ory of micromagnetics in two dimensions. We prove a compactness result for families of uniformly bounded energy. After studying the corresponding one- dimensional profiles, we exhibit the Gamma -limit ("wall energy"), which is a variational problem on the folding of solutions of the eikonal equation \ del (g)\= 1. We prove that the minimal wall energy is twice the perimeter . (C) 2001 John Wiley & Sons, Inc.