On a shape derivative formula for the Robin $p$-Laplace eigenvalue
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929209064030208 |
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| author | A, Ardra Mallick, Mohan Sasi, Sarath |
| author_facet | A, Ardra Mallick, Mohan Sasi, Sarath |
| contents | We obtain shape derivative formulae for the first eigenvalue of the Robin $p$-Laplace operator. This result is used to study the variation of the first eigenvalue with respect to perturbations of the domain. In particular, we prove that for large values of the boundary parameter, the first eigenvalue is monotonic with respect to domain inclusion for smooth domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05183 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a shape derivative formula for the Robin $p$-Laplace eigenvalue A, Ardra Mallick, Mohan Sasi, Sarath Analysis of PDEs 35J92, 35P30, 35P99, 49R05 We obtain shape derivative formulae for the first eigenvalue of the Robin $p$-Laplace operator. This result is used to study the variation of the first eigenvalue with respect to perturbations of the domain. In particular, we prove that for large values of the boundary parameter, the first eigenvalue is monotonic with respect to domain inclusion for smooth domains. |
| title | On a shape derivative formula for the Robin $p$-Laplace eigenvalue |
| topic | Analysis of PDEs 35J92, 35P30, 35P99, 49R05 |
| url | https://arxiv.org/abs/2208.05183 |