Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915625418358784 |
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| author | Shen, Zhongwei |
| author_facet | Shen, Zhongwei |
| contents | Consider the Dirichlet-to-Neumann map $Λ_β$ associated with the Schrödinger operator $(D+β\A)^2$ with a magnetic potential in a bounded Lipschitz domain $Ω$, where $β>1$ is the field strength parameter. Assume that the magnetic field $\B=\nabla \times \A$ is of finite type. We show that if $β>β_0$, the ground state for $Λ_β$ decays exponentially away from a neighborhood of the subset of $\partialΩ$, on which $\B$ vanishes to the maximal order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14054 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian Shen, Zhongwei Analysis of PDEs 35P20, 35Q40 Consider the Dirichlet-to-Neumann map $Λ_β$ associated with the Schrödinger operator $(D+β\A)^2$ with a magnetic potential in a bounded Lipschitz domain $Ω$, where $β>1$ is the field strength parameter. Assume that the magnetic field $\B=\nabla \times \A$ is of finite type. We show that if $β>β_0$, the ground state for $Λ_β$ decays exponentially away from a neighborhood of the subset of $\partialΩ$, on which $\B$ vanishes to the maximal order. |
| title | Exponential Decays of Steklov Eigenfunctions for the Magnetic Laplacian |
| topic | Analysis of PDEs 35P20, 35Q40 |
| url | https://arxiv.org/abs/2511.14054 |