Geodesic
Équations aux dérivées partielles
Uniqueness of bounded solutions to p-Laplace problems in strips
Le, Phuong1, 2 
1 Faculty of Economic Mathematics, University of Economics and Law, Ho Chi Minh City, Vietnam
2 Vietnam National University, Ho Chi Minh City, Vietnam
Comptes Rendus. Mathématique, Tome 361 (2023) no. G4, pp. 795-801

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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 ∈(0,+∞], 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 <+∞ 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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DOI : 10.5802/crmath.442
Classification : 35J92, 35A01, 35A02, 35B06
Keywords: $p$-Laplace equation, uniqueness, monotonicity, 1D symmetry

Le, Phuong 1, 2

1 Faculty of Economic Mathematics, University of Economics and Law, Ho Chi Minh City, Vietnam
2 Vietnam National University, Ho Chi Minh City, Vietnam
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Uniqueness of bounded solutions to $p${-Laplace} problems in strips},
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Le, Phuong. Uniqueness of bounded solutions to $p$-Laplace problems in strips. Comptes Rendus. Mathématique, Tome 361 (2023) no. G4, pp. 795-801. doi: 10.5802/crmath.442

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