Calculus of Variations and Geometric Measure Theory

L. Ambrosio - M. Lecumberry - T. Rivière

A viscosity property of minimizing micromagnetic configurations

created on 18 Mar 2002
modified on 17 Dec 2002


Accepted Paper

Inserted: 18 mar 2002
Last Updated: 17 dec 2002

Journal: Communications on Pure and Applied Mathematics
Year: 2002


We study the limit as $\epsilon\downarrow 0$ of the minimizers of a singularly perturbed problem arising in micromagnetics. Using a sign condition and a kinetic interpretation of the limit problem we show that limiting vectorfields are, after a rotation, gradients of viscosity solutions of the eikonal equation. This leads to a characterization of limiting configurations, once boundary conditions are imposed. This solves a problem left open in a previous paper by S.Serfaty and T.Riviere.

Keywords: Viscosity solutions, Micromagnetism, BV functions