April 9, 2024Open Access

An isoperimetric inequality for the first Robin-Dirichlet eigenvalue of the Laplacian

Key Points

Key points are not available for this paper at this time.

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 the domains with fixed measure, outer perimeter and inner (n-1) ^th quermassintegral.

Read Full Paperexternally

Mark Helpful

Bookmark

Relay

View Full Paper

Cite This Study

Gavitone et al. (Tue,) studied this question.

synapsesocial.com/papers/68e6febab6db64358767909f https://doi.org/https://doi.org/10.48550/arxiv.2404.06607

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1A stability result for the first Robin–Neumann eigenvalue: A double perturbation approach2024 · 3 citations
2A spectral isoperimetric inequality on the n-sphere for the Robin-Laplacian with negative boundary parameter2024
3Geometric Optimization of the First Robin Eigenvalue in Exterior Domains2024
4On asymptotics of Robin eigenvalues in the Dirichlet limit2024
5On asymptotics of Robin eigenvalues in the Dirichlet limit2025 · 1 citations

Mark Helpful

Bookmark

Relay

View Full Paper