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MiS Preprint
106/2007

Regularity of domain walls in magnetic nanowires

Katharina Kühn

Abstract

This paper investigates regularity properties of energy minimising 180 degree domain walls in magnetic nanowires. For small radii we prove uniform bounds in $C^{1,\beta}$. Uniform bounds imply convergence in strong norms and are important for the step from statics to dynamics.

First we show the convergence of minimisers in $H^1$ and a bound on the rate of convergence of the minimal energies. Then we use the notion of almost minimisers to prove $C^{0,\alpha}$ estimates and the Morrey-Campanato approach to get uniform $C^{1,\beta}$ estimates.

Received:
Dec 13, 2007
Published:
Dec 13, 2007
MSC Codes:
47J30, 82D40
Keywords:
micromagnetism, regularity

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Preprint
2007 Repository Open Access
Katharina Kühn

Regularity of domain walls in magnetic nanowires