Submitted Paper

Inserted: 12 nov 2024
Last Updated: 12 nov 2024

Year: 2024

Abstract:

In this paper we prove a strong two-scale approximation result for sphere-valued maps in \(L^2(\Omega;W^{1,2}_0(Q_0;\mathbb{S}^2))\), where \(\Omega\subset \mathbb{R}^3\) is an open domain and \(Q_0\subset Q\) an open subset of the unit cube \(Q=(0,1)^3\). The proof relies on a generalization of the seminal argument by F. Bethuel and X.M. Zheng to the two-scale setting. We then present an application to a variational problem in high-contrast micromagnetics.

Keywords: Two-scale convergence, manifold-valued Sobolev spaces, Sard's lemma, high-contrast homogenization

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