| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 111 | |
| Number of page(s) | 15 | |
| DOI | https://doi.org/10.1051/cocv/2020033 | |
| Published online | 10 December 2020 | |
Sharp estimates for the first p-Laplacian eigenvalue and for the p-torsional rigidity on convex sets with holes
1
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli studi di Napoli Federico II Via Cintia, Complesso Universitario Monte S. Angelo,
80126
Napoli, Italy.
2
Dipartimento di Ingegneria Elettrica e dell’Informazione “M. Scarano”, Università degli Studi di Cassino e del Lazio Meridionale Via G. Di Biasio n. 43,
03043
Cassino (FR), Italy.
* Corresponding author: gianpaolo.piscitelli@unicas.it
Received:
14
October
2019
Accepted:
25
May
2020
We study, in dimension n ≥ 2, the eigenvalue problem and the torsional rigidity for the p-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.
Mathematics Subject Classification: 35J25 / 35J92 / 35P15 / 47J30
Key words: Nonlinear eigenvalue problems / torsional rigidity / mixed boundary conditions / optimal estimates
© EDP Sciences, SMAI 2020
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