A geometric approximation of non-local interface and boundary conditions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911019290329088 |
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| author | Exner, Pavel Khrabustovskyi, Andrii |
| author_facet | Exner, Pavel Khrabustovskyi, Andrii |
| contents | We analyze an approximation of a Laplacian subject to non-local interface conditions of a $δ'$-type by Neumann Laplacians on a family of Riemannian manifolds with a sieve-like structure. We establish a (kind of) resolvent convergence for such operators, which in turn implies the convergence of spectra and eigenspaces, and demonstrate convergence of the corresponding semigroups. Moreover, we provide an explicit example of a manifold allowing to realize any prescribed integral kernel appearing in that interface conditions. Finally, we extend the discussion to similar approximations for the Laplacian with non-local Robin-type boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19016 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A geometric approximation of non-local interface and boundary conditions Exner, Pavel Khrabustovskyi, Andrii Analysis of PDEs Mathematical Physics Spectral Theory 35B27, 35B40, 35P05, 47A55 We analyze an approximation of a Laplacian subject to non-local interface conditions of a $δ'$-type by Neumann Laplacians on a family of Riemannian manifolds with a sieve-like structure. We establish a (kind of) resolvent convergence for such operators, which in turn implies the convergence of spectra and eigenspaces, and demonstrate convergence of the corresponding semigroups. Moreover, we provide an explicit example of a manifold allowing to realize any prescribed integral kernel appearing in that interface conditions. Finally, we extend the discussion to similar approximations for the Laplacian with non-local Robin-type boundary conditions. |
| title | A geometric approximation of non-local interface and boundary conditions |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory 35B27, 35B40, 35P05, 47A55 |
| url | https://arxiv.org/abs/2505.19016 |