Limiting domain wall energy for a problem related to micromagnetics
Tristan Rivi�re, Stéphane Serfaty · Communications on Pure and Applied Mathematics · 2001
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.