Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains
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arXiv
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| Format: | Preprint |
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2025
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| author | Helffer, Bernard Kachmar, Ayman Nicoleau, Francois |
| author_facet | Helffer, Bernard Kachmar, Ayman Nicoleau, Francois |
| contents | Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity as the magnetic field tends to infinity. More precisely, we prove refined conjectures for general two dimensional domains, based on the analysis in the case of the half-plane and the disk by two of us (B.H. and F.N.). We also extend our analysis to the three dimensional case, and explore a connection with the eigenvalue asymptotics of the magnetic Robin Laplacian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains Helffer, Bernard Kachmar, Ayman Nicoleau, Francois Mathematical Physics Analysis of PDEs Spectral Theory Primary 58J50, Secondary 35P20 Inspired by a paper by T. Chakradhar, K. Gittins, G. Habib and N. Peyerimhoff, we analyze their conjecture that the ground state energy of the magnetic Dirichlet-to-Neumann operator tends to infinity as the magnetic field tends to infinity. More precisely, we prove refined conjectures for general two dimensional domains, based on the analysis in the case of the half-plane and the disk by two of us (B.H. and F.N.). We also extend our analysis to the three dimensional case, and explore a connection with the eigenvalue asymptotics of the magnetic Robin Laplacian. |
| title | Asymptotics for the magnetic Dirichlet-to-Neumann eigenvalues in general domains |
| topic | Mathematical Physics Analysis of PDEs Spectral Theory Primary 58J50, Secondary 35P20 |
| url | https://arxiv.org/abs/2501.00947 |