Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917354319904768 |
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| author | DelaTorre, Azahara Mancini, Gabriele Pistoia, Angela Provenzano, Luigi |
| author_facet | DelaTorre, Azahara Mancini, Gabriele Pistoia, Angela Provenzano, Luigi |
| contents | We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in presence of a singular term. We use conformal transformations to rewrite the linearized equation as a Steklov eigenvalue problem posed in a bounded domain, which is defined either by an intersection or a union of two disks. We conclude by proving the simplicity of the corresponding eigenvalue. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14119 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation DelaTorre, Azahara Mancini, Gabriele Pistoia, Angela Provenzano, Luigi Analysis of PDEs 35R11 (35B33, 45G05, 35A02) We prove the non-degeneracy of solutions to a fractional and singular Liouville equation defined on the whole real line in presence of a singular term. We use conformal transformations to rewrite the linearized equation as a Steklov eigenvalue problem posed in a bounded domain, which is defined either by an intersection or a union of two disks. We conclude by proving the simplicity of the corresponding eigenvalue. |
| title | Non-degeneracy of the bubble in a fractional and singular 1D Liouville equation |
| topic | Analysis of PDEs 35R11 (35B33, 45G05, 35A02) |
| url | https://arxiv.org/abs/2404.14119 |