Uniqueness of bounded solutions to $p$-Laplace problems in strips
We consider a $p$-Laplace problem in a strip with two-constant boundary Dirichlet conditions. We show that if the width of the strip is smaller than some $d_0\in (0,+\infty ]$, then the problem admits a unique bounded solution, which is strictly monotone. Hence this unique solution is one-dimensiona...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-05-01
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| Series: | Comptes Rendus. Mathématique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.442/ |
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| Summary: | We consider a $p$-Laplace problem in a strip with two-constant boundary Dirichlet conditions. We show that if the width of the strip is smaller than some $d_0\in (0,+\infty ]$, then the problem admits a unique bounded solution, which is strictly monotone. Hence this unique solution is one-dimensional symmetric and belongs to the $C^2$ class. We also show that the problem has no bounded solution in the case that $d_0<+\infty $ and the width of the strip is larger than or equal to $d_0$. An analogous rigidity result in the whole space was obtained recently by Esposito et al. [8] |
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| ISSN: | 1778-3569 |