A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle

Gloria Paoli; Gianpaolo Piscitelli; Rossanno Sannipoli

doi:10.3934/cpaa.2020261

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2021, Volume 20, Issue 1: 145-158. Doi: 10.3934/cpaa.2020261

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A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle

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
^* Corresponding author

Received: April 30, 2020

Revised: July 31, 2020

Early access: October 2020

Published: January 2021

This work has been partially supported by GNAMPA of INdAM and by Progetto di eccellenza "Sistemi distribuiti intelligenti" of Dipartimento di Ingegneria Elettrica e dell'Informazione "M. Scarano"

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Abstract

In this paper we study the first Steklov-Laplacian eigenvalue with an internal fixed spherical obstacle. We prove that the spherical shell locally maximizes the first eigenvalue among nearly spherical sets when both the internal ball and the volume are fixed.

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Mathematics Subject Classification: Primary: 35J25, 35P15; Secondary: 28A75.

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References

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