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.
|Original language||English (US)|
|Number of pages||45|
|Journal||Communications on Pure and Applied Mathematics|
|State||Published - Mar 2001|
ASJC Scopus subject areas
- Applied Mathematics