A Sharp Bound for the First Robin–Dirichlet Eigenvalue

Nunzia Gavitone () and Gianpaolo Piscitelli ()
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Nunzia Gavitone: Università degli studi di Napoli Federico II
Gianpaolo Piscitelli: Università degli Studi di Napoli Parthenope

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 27, 745-766

Abstract: Abstract In this paper, we study the first eigenvalue of the Laplacian on doubly connected domains when Robin and Dirichlet conditions are imposed on the outer and the inner part of the boundary, respectively. We provide that the spherical shell reaches the maximum of the first eigenvalue of this problem among a suitable class of domains when the measure, the outer perimeter and inner $$(n-1)$$ ( n - 1 ) th quermassintegral are fixed.

Keywords: Laplacian eigenvalues; Robin–Dirichlet boundary conditions; Inner parallel method; Web-functions; 35B40; 35J25; 35P15 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02531-1

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