Inserted: 18 mar 2002
Last Updated: 17 dec 2002
Journal: Communications on Pure and Applied Mathematics
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