We consider a -Laplace problem in a strip with two-constant boundary Dirichlet conditions. We show that if the width of the strip is smaller than some , then the problem admits a unique bounded solution, which is strictly monotone. Hence this unique solution is one-dimensional symmetric and belongs to the class. We also show that the problem has no bounded solution in the case that and the width of the strip is larger than or equal to . An analogous rigidity result in the whole space was obtained recently by Esposito et al. [8]
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Keywords: $p$-Laplace equation, uniqueness, monotonicity, 1D symmetry
Le, Phuong 1, 2
CC-BY 4.0
@article{CRMATH_2023__361_G4_795_0,
author = {Le, Phuong},
title = {Uniqueness of bounded solutions to $p${-Laplace} problems in strips},
journal = {Comptes Rendus. Math\'ematique},
pages = {795--801},
year = {2023},
publisher = {Acad\'emie des sciences, Paris},
volume = {361},
number = {G4},
doi = {10.5802/crmath.442},
language = {en},
url = {https://www.numdam.org/articles/10.5802/crmath.442/}
}
TY - JOUR AU - Le, Phuong TI - Uniqueness of bounded solutions to $p$-Laplace problems in strips JO - Comptes Rendus. Mathématique PY - 2023 SP - 795 EP - 801 VL - 361 IS - G4 PB - Académie des sciences, Paris UR - https://www.numdam.org/articles/10.5802/crmath.442/ DO - 10.5802/crmath.442 LA - en ID - CRMATH_2023__361_G4_795_0 ER -
%0 Journal Article %A Le, Phuong %T Uniqueness of bounded solutions to $p$-Laplace problems in strips %J Comptes Rendus. Mathématique %D 2023 %P 795-801 %V 361 %N G4 %I Académie des sciences, Paris %U https://www.numdam.org/articles/10.5802/crmath.442/ %R 10.5802/crmath.442 %G en %F CRMATH_2023__361_G4_795_0
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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