Abstract
In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analogous estimate is obtained for the corresponding torsional rigidity problem.
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Acknowledgements
This work has been partially supported by a MIUR-PRIN 2017 grant “Qualitative and quantitative aspects of nonlinear PDE’s” and by GNAMPA of INdAM. The second author (G.P.) was also supported by Progetto di eccellenza “Sistemi distribuiti intelligenti”of Dipartimento di Ingegneria Elettrica e dell’Informazione “M. Scarano”.
Funding
Open access funding provided by Universit`a degli Studi di Napoli Federico II within the CRUI-CARE Agreement.
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Pietra, F.D., Piscitelli, G. An Optimal Bound for Nonlinear Eigenvalues and Torsional Rigidity on Domains with Holes. Milan J. Math. 88, 373–384 (2020). https://doi.org/10.1007/s00032-020-00320-9
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DOI: https://doi.org/10.1007/s00032-020-00320-9
Mathematics Subject Classification (2010)
- 35P15
- 47J30
- 35J92
- 35J25
Keywords
- Nonlinear eigenvalue problems
- torsional rigidity
- mixed boundary conditions
- optimal estimates