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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.23917 |
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| _version_ | 1866916464158572544 |
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| author | Abatangelo, Laura Felli, Veronica |
| author_facet | Abatangelo, Laura Felli, Veronica |
| contents | We study double eigenvalues of Aharonov-Bohm operators with Dirichlet boundary conditions in planar domains containing the origin. We focus on the behavior of double eigenvalues when the potential's circulation is a fixed half-integer number and the operator's pole is moving on straight lines in a neighborhood of the origin. We prove that bifurcation occurs if the pole is moving along straight lines in a certain number of cones with positive measure. More precise information is given for symmetric domains; in particular, in the special case of the disk, any eigenvalue is double if the pole is located at the centre, but there exists a whole neighborhood where it bifurcates into two distinct branches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole Abatangelo, Laura Felli, Veronica Analysis of PDEs We study double eigenvalues of Aharonov-Bohm operators with Dirichlet boundary conditions in planar domains containing the origin. We focus on the behavior of double eigenvalues when the potential's circulation is a fixed half-integer number and the operator's pole is moving on straight lines in a neighborhood of the origin. We prove that bifurcation occurs if the pole is moving along straight lines in a certain number of cones with positive measure. More precise information is given for symmetric domains; in particular, in the special case of the disk, any eigenvalue is double if the pole is located at the centre, but there exists a whole neighborhood where it bifurcates into two distinct branches. |
| title | Bifurcation of double eigenvalues for Aharonov-Bohm operators with a moving pole |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.23917 |