Rectifiability of entropy defect measures in a micromagnetics model

Abstract

We study the fine properties of a class of weak solutions $u$ of the eikonal equation arising as asymptotic domain of a family of energy functionals introduced in (Rivière T, Serfaty S. Limiting domain wall energy for a problem related to micromagnetics. Comm Pure Appl Math 2001; 54(3):294-338). In particular we prove that the entropy defect measure associated to $u$ is concentrated on a 1-rectifiable set, which detects the jump-type discontinuities of $u$.

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• Characterization of minimizers of Aviles-Giga functionals in special domains