Inequalities for eigenvalues of Schrödinger operators with mixed boundary conditions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929481221931008 |
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| author | Aldeghi, Nausica |
| author_facet | Aldeghi, Nausica |
| contents | We consider the eigenvalue problem for the Schrödinger operator on bounded, convex domains with mixed boundary conditions, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. We prove inequalities between the lowest eigenvalues corresponding to two different choices of such boundary conditions on both planar and higher-dimensional domains. We also prove an inequality between higher order mixed eigenvalues and pure Dirichlet eigenvalues on multidimensional polyhedral domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00019 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inequalities for eigenvalues of Schrödinger operators with mixed boundary conditions Aldeghi, Nausica Spectral Theory Mathematical Physics Analysis of PDEs We consider the eigenvalue problem for the Schrödinger operator on bounded, convex domains with mixed boundary conditions, where a Dirichlet boundary condition is imposed on a part of the boundary and a Neumann boundary condition on its complement. We prove inequalities between the lowest eigenvalues corresponding to two different choices of such boundary conditions on both planar and higher-dimensional domains. We also prove an inequality between higher order mixed eigenvalues and pure Dirichlet eigenvalues on multidimensional polyhedral domains. |
| title | Inequalities for eigenvalues of Schrödinger operators with mixed boundary conditions |
| topic | Spectral Theory Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2409.00019 |