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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Académie des sciences
2023-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.442/ |
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| author | Le, Phuong |
| author_facet | Le, Phuong |
| author_sort | Le, Phuong |
| collection | DOAJ |
| description | 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] |
| format | Article |
| id | doaj-art-7ab96eabf5884dff95e7a45873cc3b35 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-7ab96eabf5884dff95e7a45873cc3b352025-02-07T11:07:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-05-01361G479580110.5802/crmath.44210.5802/crmath.442Uniqueness of bounded solutions to $p$-Laplace problems in stripsLe, Phuong0https://orcid.org/0000-0003-4724-7118Faculty of Economic Mathematics, University of Economics and Law, Ho Chi Minh City, Vietnam; Vietnam National University, Ho Chi Minh City, VietnamWe 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]https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.442/$p$-Laplace equationuniquenessmonotonicity1D symmetry |
| spellingShingle | Le, Phuong Uniqueness of bounded solutions to $p$-Laplace problems in strips Comptes Rendus. Mathématique $p$-Laplace equation uniqueness monotonicity 1D symmetry |
| title | Uniqueness of bounded solutions to $p$-Laplace problems in strips |
| title_full | Uniqueness of bounded solutions to $p$-Laplace problems in strips |
| title_fullStr | Uniqueness of bounded solutions to $p$-Laplace problems in strips |
| title_full_unstemmed | Uniqueness of bounded solutions to $p$-Laplace problems in strips |
| title_short | Uniqueness of bounded solutions to $p$-Laplace problems in strips |
| title_sort | uniqueness of bounded solutions to p laplace problems in strips |
| topic | $p$-Laplace equation uniqueness monotonicity 1D symmetry |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.442/ |
| work_keys_str_mv | AT lephuong uniquenessofboundedsolutionstoplaplaceproblemsinstrips |