MiS Preprint Repository

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.