On localisation of eigenfunctions of the Laplace operator
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929686778478592 |
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| author | Berg, Michiel van den Bucur, Dorin |
| author_facet | Berg, Michiel van den Bucur, Dorin |
| contents | We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a sequence of first Dirichlet eigenfunctions for a wide class of elongating horn-shaped domains. We give examples of sequences of simply connected, planar, polygonal domains for which the corresponding sequence of first eigenfunctions with either Dirichlet, or Neumann, boundary conditions $κ$-localise in $L^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_00479 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On localisation of eigenfunctions of the Laplace operator Berg, Michiel van den Bucur, Dorin Spectral Theory We prove (i) a simple sufficient geometric condition for localisation of a sequence of first Dirichlet eigenfunctions provided the corresponding Dirichlet Laplacians satisfy a uniform Hardy inequality, and (ii) localisation of a sequence of first Dirichlet eigenfunctions for a wide class of elongating horn-shaped domains. We give examples of sequences of simply connected, planar, polygonal domains for which the corresponding sequence of first eigenfunctions with either Dirichlet, or Neumann, boundary conditions $κ$-localise in $L^2$. |
| title | On localisation of eigenfunctions of the Laplace operator |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2206.00479 |