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

Abstract

In this paper we study the first Steklov-Laplacian eigenvalue with an internal fixed spherichal 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.

References in corpus (4)

• On the second Dirichlet eigenvalue of some nonlinear anisotropic elliptic operators
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• A sharp weighted anisotropic Poincaré inequality for convex domains
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Cited by in corpus (2)

• An isoperimetric inequality for the first Steklov-Dirichlet Laplacian eigenvalue of convex sets with a spherical hole
• Shape monotonicity of the first Steklov-Dirichlet eigenvalue on eccentric annuli