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A Sharp Bound for the First Robin–Dirichlet Eigenvalue

Author

Listed:
  • Nunzia Gavitone

    (Università degli studi di Napoli Federico II)

  • Gianpaolo Piscitelli

    (Università degli Studi di Napoli Parthenope)

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.

Suggested Citation

  • Nunzia Gavitone & Gianpaolo Piscitelli, 2024. "A Sharp Bound for the First Robin–Dirichlet Eigenvalue," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 745-766, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02531-1
    DOI: 10.1007/s10957-024-02531-1
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    References listed on IDEAS

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    1. Catherine Bandle & Alfred Wagner, 2015. "Second Domain Variation for Problems with Robin Boundary Conditions," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 430-463, November.
    2. Anisa M. H. Chorwadwala & Souvik Roy, 2020. "How to Place an Obstacle Having a Dihedral Symmetry Inside a Disk so as to Optimize the Fundamental Dirichlet Eigenvalue," Journal of Optimization Theory and Applications, Springer, vol. 184(1), pages 162-187, January.
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