TY - JOUR
T1 - Limiting domain wall energy for a problem related to micromagnetics
AU - Rivière, Tristan
AU - Serfaty, Sylvia
PY - 2001/3
Y1 - 2001/3
N2 - 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.
AB - 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.
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U2 - 10.1002/1097-0312(200103)54:3<294::AID-CPA2>3.0.CO;2-S
DO - 10.1002/1097-0312(200103)54:3<294::AID-CPA2>3.0.CO;2-S
M3 - Article
AN - SCOPUS:0035580604
SN - 0010-3640
VL - 54
SP - 294
EP - 338
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
IS - 3
ER -