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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.04584 |
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| _version_ | 1866914179736141824 |
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| author | Chen, Zhijie Song, Zhen Zou, Wenming |
| author_facet | Chen, Zhijie Song, Zhen Zou, Wenming |
| contents | In this paper, we prove a quantitative refinement of the isoperimetric type inequality for the second Robin eigenvalue with negative boundary parameters established by Freitas and Laugesen [Amer.J.Math.143 (2021), no.3, 969-994].Such new stability estimate is proved when the boundary parameter is not too far from 0.By constructing a suitable family of nearly spherical domains, we prove that the exponent for the Fraenkel asymmetry in this quantitative type inequality is sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04584 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp stability on the second Robin eigenvalue with negative boundary parameters Chen, Zhijie Song, Zhen Zou, Wenming Analysis of PDEs In this paper, we prove a quantitative refinement of the isoperimetric type inequality for the second Robin eigenvalue with negative boundary parameters established by Freitas and Laugesen [Amer.J.Math.143 (2021), no.3, 969-994].Such new stability estimate is proved when the boundary parameter is not too far from 0.By constructing a suitable family of nearly spherical domains, we prove that the exponent for the Fraenkel asymmetry in this quantitative type inequality is sharp. |
| title | Sharp stability on the second Robin eigenvalue with negative boundary parameters |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.04584 |