Concentration of eigenfunctions on singular Riemannian manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913565614538752 |
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| author | Dietze, Charlotte Read, Larry |
| author_facet | Dietze, Charlotte Read, Larry |
| contents | We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter regime, we identify the rate of concentration and profile of the high-frequency eigenfunctions that accumulate at the boundary. We give an application to acoustic modes on gas planets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20563 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Concentration of eigenfunctions on singular Riemannian manifolds Dietze, Charlotte Read, Larry Analysis of PDEs Earth and Planetary Astrophysics Mathematical Physics Spectral Theory Primary: 58C40, Secondary: 53C17, 35P20 We consider a compact Riemannian manifold with boundary and a metric that is singular at the boundary. The associated Laplace-Beltrami operator is of the form of a Grushin operator plus a singular potential. In a supercritical parameter regime, we identify the rate of concentration and profile of the high-frequency eigenfunctions that accumulate at the boundary. We give an application to acoustic modes on gas planets. |
| title | Concentration of eigenfunctions on singular Riemannian manifolds |
| topic | Analysis of PDEs Earth and Planetary Astrophysics Mathematical Physics Spectral Theory Primary: 58C40, Secondary: 53C17, 35P20 |
| url | https://arxiv.org/abs/2410.20563 |