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arXiv · 2411.07838

Two-scale density of almost smooth functions in sphere-valued Sobolev spaces: A high-contrast extension of the Bethuel-Zheng theory

Elisa Davoli·Leon Happ
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Abstract

In this paper we prove a strong two-scale approximation result for sphere-valued maps in $L^2(Ω;W^{1,2}_0(Q_0;\mathbb{S}^2))$, where $Ω\subset \mathbb{R}^3$ 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.

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Elisa Davoli, Leon Happ. 2024-11-12. Two-scale density of almost smooth functions in sphere-valued Sobolev spaces: A high-contrast extension of the Bethuel-Zheng theory. https://arxiv.org/abs/2411.07838

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