A Liouville-type theorem for the Lane-Emden equation in a half-space
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866913810744344576 |
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| author | Dupaigne, Louis Sirakov, Boyan Souplet, Philippe |
| author_facet | Dupaigne, Louis Sirakov, Boyan Souplet, Philippe |
| contents | We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_11466 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Liouville-type theorem for the Lane-Emden equation in a half-space Dupaigne, Louis Sirakov, Boyan Souplet, Philippe Analysis of PDEs We prove that the Dirichlet problem for the Lane-Emden equation in a half-space has no positive solution which is monotone in the normal direction. As a consequence, this problem does not admit any positive classical solution which is bounded on finite strips. This question has a long history and our result solves a long-standing open problem. Such a nonexistence result was previously available only for bounded solutions, or under a restriction on the power in the nonlinearity. The result extends to general convex nonlinearities. |
| title | A Liouville-type theorem for the Lane-Emden equation in a half-space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2003.11466 |