Shape sensitivity analysis of Neumann-Poincaré eigenvalues
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908293956370432 |
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| author | Riva, Matteo Dalla Lamberti, Pier Domenico Luzzini, Paolo Musolino, Paolo |
| author_facet | Riva, Matteo Dalla Lamberti, Pier Domenico Luzzini, Paolo Musolino, Paolo |
| contents | This paper concerns the eigenvalues of the Neumann-Poincaré operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and prove that the map associating the support's shape to the eigenvalues is real-analytic. We then compute its first derivative and present applications of the resulting formula. The proposed method allows for handling infinite-dimensional perturbation parameters for multiple eigenvalues and perturbations that are not necessarily in the normal direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shape sensitivity analysis of Neumann-Poincaré eigenvalues Riva, Matteo Dalla Lamberti, Pier Domenico Luzzini, Paolo Musolino, Paolo Analysis of PDEs Optimization and Control Spectral Theory 31A10, 31B10, 35B20, 35P99, 47A10, 47A11, 47A55 This paper concerns the eigenvalues of the Neumann-Poincaré operator, a boundary integral operator associated with the harmonic double-layer potential. Specifically, we examine how the eigenvalues depend on the support of integration and prove that the map associating the support's shape to the eigenvalues is real-analytic. We then compute its first derivative and present applications of the resulting formula. The proposed method allows for handling infinite-dimensional perturbation parameters for multiple eigenvalues and perturbations that are not necessarily in the normal direction. |
| title | Shape sensitivity analysis of Neumann-Poincaré eigenvalues |
| topic | Analysis of PDEs Optimization and Control Spectral Theory 31A10, 31B10, 35B20, 35P99, 47A10, 47A11, 47A55 |
| url | https://arxiv.org/abs/2504.00696 |