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Limiting domain wall energy for a problem related to micromagnetics
Author(s) -
Rivière Tristan,
Serfaty Sylvia
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/1097-0312(200103)54:3<294::aid-cpa2>3.0.co;2-s
Subject(s) - micromagnetics , eikonal equation , compact space , mathematics , limit (mathematics) , limiting , bounded function , energy (signal processing) , domain (mathematical analysis) , mathematical analysis , uniform boundedness , preprint , physics , quantum mechanics , magnetization , mechanical engineering , statistics , magnetic field , engineering
We study the asymptotic limit of a family of functionals related to the theory 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 Γ‐limit (“wall energy”), which is a variational problem on the folding of solutions of the eikonal equation |∇ g | = 1. We prove that the minimal wall energy is twice the perimeter. © 2001 John Wiley & Sons, Inc.