On the first eigenvalue of Liouville-type problems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910836045381632 |
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| author | Bartolucci, Daniele Cosentino, Paolo Jevnikar, Aleks Lin, Chang-Shou |
| author_facet | Bartolucci, Daniele Cosentino, Paolo Jevnikar, Aleks Lin, Chang-Shou |
| contents | The aim of this note is to study the spectrum of a linearized Liouville-type problem, characterizing the case in which the first eigenvalue is zero. Interestingly enough, we obtain also point-wise information on the associated first eigenfunction. To this end, we refine the Alexandrov-Bol inequality suitable for our problem and characterize its equality case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10256 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the first eigenvalue of Liouville-type problems Bartolucci, Daniele Cosentino, Paolo Jevnikar, Aleks Lin, Chang-Shou Analysis of PDEs 35J61, 35A23, 35P15 The aim of this note is to study the spectrum of a linearized Liouville-type problem, characterizing the case in which the first eigenvalue is zero. Interestingly enough, we obtain also point-wise information on the associated first eigenfunction. To this end, we refine the Alexandrov-Bol inequality suitable for our problem and characterize its equality case. |
| title | On the first eigenvalue of Liouville-type problems |
| topic | Analysis of PDEs 35J61, 35A23, 35P15 |
| url | https://arxiv.org/abs/2306.10256 |