On the Laplace operator with a weak magnetic field in exterior domains
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914814800953344 |
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| author | Kachmar, Ayman Lotoreichik, Vladimir Sundqvist, Mikael |
| author_facet | Kachmar, Ayman Lotoreichik, Vladimir Sundqvist, Mikael |
| contents | We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak magnetic field limit. For the exterior of a star-shaped domain, we obtain an asymptotic upper bound on the lowest eigenvalue in the weak field limit, involving the $4$-moment, and optimal for the case of the disk. Moreover, we prove that, for moderate magnetic fields, the exterior of the disk is a local maximizer for the lowest eigenvalue under a $p$-moment constraint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18154 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Laplace operator with a weak magnetic field in exterior domains Kachmar, Ayman Lotoreichik, Vladimir Sundqvist, Mikael Spectral Theory Mathematical Physics Analysis of PDEs 35P15, 58J50, 34L15, 35Q40 We study the magnetic Laplacian in a two-dimensional exterior domain with Neumann boundary condition and uniform magnetic field. For the exterior of the disk we establish accurate asymptotics of the low-lying eigenvalues in the weak magnetic field limit. For the exterior of a star-shaped domain, we obtain an asymptotic upper bound on the lowest eigenvalue in the weak field limit, involving the $4$-moment, and optimal for the case of the disk. Moreover, we prove that, for moderate magnetic fields, the exterior of the disk is a local maximizer for the lowest eigenvalue under a $p$-moment constraint. |
| title | On the Laplace operator with a weak magnetic field in exterior domains |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs 35P15, 58J50, 34L15, 35Q40 |
| url | https://arxiv.org/abs/2405.18154 |