An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911462734168064 |
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| author | Gao, Yi Wang, Kui Zhu, Anqiang |
| author_facet | Gao, Yi Wang, Kui Zhu, Anqiang |
| contents | In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our main theorem states that the ball centered at the origin maximizes the second Robin eigenvalue among all Lipschitz bounded domains of prescribed weighted measure and symmetric about the origin for a range of negative Robin parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19456 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian Gao, Yi Wang, Kui Zhu, Anqiang Analysis of PDEs Spectral Theory 35P15 In this paper, we investigate a shape optimization problem for the second Robin eigenvalue of the weighted Laplacian on bounded Lipschitz domains symmetric about the origin. Our main theorem states that the ball centered at the origin maximizes the second Robin eigenvalue among all Lipschitz bounded domains of prescribed weighted measure and symmetric about the origin for a range of negative Robin parameters. |
| title | An isoperimetric inequality for the second Robin eigenvalue of the Weighted Laplacian |
| topic | Analysis of PDEs Spectral Theory 35P15 |
| url | https://arxiv.org/abs/2602.19456 |