Two-scale density of almost smooth functions in sphere-valued Sobolev spaces: A high-contrast extension of the Bethuel-Zheng theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916478293377024 |
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| author | Davoli, Elisa Happ, Leon |
| author_facet | Davoli, Elisa Happ, Leon |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_07838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-scale density of almost smooth functions in sphere-valued Sobolev spaces: A high-contrast extension of the Bethuel-Zheng theory Davoli, Elisa Happ, Leon Analysis of PDEs 46E35, 35B27, 74Q05 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. |
| title | Two-scale density of almost smooth functions in sphere-valued Sobolev spaces: A high-contrast extension of the Bethuel-Zheng theory |
| topic | Analysis of PDEs 46E35, 35B27, 74Q05 |
| url | https://arxiv.org/abs/2411.07838 |