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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.03690 |
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| _version_ | 1866908352078938112 |
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| author | Shen, Zhongwei |
| author_facet | Shen, Zhongwei |
| contents | This paper is concerned with spectrum properties of the magnetic Laplacian with a higher-order vanishing magnetic field in a bounded domain. We study the asymptotic behaviors of ground state energies for the Dirichlet Laplacian, the Neumann Laplacian, and the Dirichlet-to-Neumann operator, as the field strength parameter $β$ goes to infinite. Assume that the magnetic field does not vanish to infinite order, we establish the leading orders of $β$. We also obtain the first terms in the asymptotic expansions with remainder estimates under additional assumptions on an invariant subspace for a Taylor polynomial of the magnetic field. Our aim is to provide a unified approach to all three cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03690 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Magnetic Laplacian with a Higher-order Vanishing Magnetic Field in a Bounded Domain Shen, Zhongwei Analysis of PDEs 35P25 This paper is concerned with spectrum properties of the magnetic Laplacian with a higher-order vanishing magnetic field in a bounded domain. We study the asymptotic behaviors of ground state energies for the Dirichlet Laplacian, the Neumann Laplacian, and the Dirichlet-to-Neumann operator, as the field strength parameter $β$ goes to infinite. Assume that the magnetic field does not vanish to infinite order, we establish the leading orders of $β$. We also obtain the first terms in the asymptotic expansions with remainder estimates under additional assumptions on an invariant subspace for a Taylor polynomial of the magnetic field. Our aim is to provide a unified approach to all three cases. |
| title | The Magnetic Laplacian with a Higher-order Vanishing Magnetic Field in a Bounded Domain |
| topic | Analysis of PDEs 35P25 |
| url | https://arxiv.org/abs/2505.03690 |