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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.01214 |
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| _version_ | 1866909137495916544 |
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| author | Dieb, Abdelrazek Ianni, Isabella Saldaña, Alberto |
| author_facet | Dieb, Abdelrazek Ianni, Isabella Saldaña, Alberto |
| contents | We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains. Our proofs rely on uniform estimates on growing domains, on the uniqueness and nondegeneracy of the ground state of the problem in RN , and on a new symmetry characterization of the eigenfunctions of the linearized eigenvalue problem in domains which are convex in the x1 - direction and symmetric with respect to a hyperplane reflection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01214 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems Dieb, Abdelrazek Ianni, Isabella Saldaña, Alberto Analysis of PDEs 35S15, 35A02, 35B40 We prove the uniqueness and nondegeneracy of least-energy solutions of a fractional Dirichlet semilinear problem in sufficiently large balls and in more general symmetric domains. Our proofs rely on uniform estimates on growing domains, on the uniqueness and nondegeneracy of the ground state of the problem in RN , and on a new symmetry characterization of the eigenfunctions of the linearized eigenvalue problem in domains which are convex in the x1 - direction and symmetric with respect to a hyperplane reflection. |
| title | Uniqueness and nondegeneracy of least-energy solutions to fractional Dirichlet problems |
| topic | Analysis of PDEs 35S15, 35A02, 35B40 |
| url | https://arxiv.org/abs/2310.01214 |