PreprintCC BY 4.0arXiv
Serrin-type overdetermined problem for the p-Laplacian with Robin boundary conditions
Abstract
Let Ω be an open bounded connected subset of ℝN, N ≥ 2, of class C2,α, for α∈ (0,1). Let p ≥ 2 and β>0. We prove the symmetry of the solution of the p-torsion problem with Robin boundary condition subject to the natural overdetermined condition coming from a shape derivative argument and to an extra condition on β and on the minimum of the principal curvatures of ∂Ω. The proof is based on some new integral identities, involving the linearized operator of the p-Laplacian applied to the standard P-function. In passing we prove some other rigidity results in the spirit of Serrin's and Alexandrov's Theorems.
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BibTeX
@misc{barbato2026serrintype,
title = {{Serrin-type overdetermined problem for the $p$-Laplacian with Robin boundary conditions}},
author = {Luca Barbato and Riccardo Molinarolo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29393},
eprint = {2609.29393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29393},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Serrin-type overdetermined problem for the p-Laplacian with Robin boundary conditions
AU - Luca Barbato
AU - Riccardo Molinarolo
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29393
UR - https://arxiv.org/abs/2609.29393
AB - Let Ω be an open bounded connected subset of ℝ^N, N ≥ 2, of class C^2,α, for α∈ (0,1). Let p ≥ 2 and β>0. We prove the symmetry of the solution of the p-torsion problem with Robin boundary condition subject to the natural overdetermined condition coming from a shape derivative argument and to an extra condition on β and on the minimum of the principal curvatures of ∂Ω. The proof is based on some new integral identities, involving the linearized operator of the p-Laplacian applied to the standard P-function. In passing we prove some other rigidity results in the spirit of Serrin's and Alexandrov's Theorems.
ER -