MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Regularity of domain walls in magnetic nanowires

Katharina Kühn


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.

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

Related publications

2007 Repository Open Access
Katharina Kühn

Regularity of domain walls in magnetic nanowires