Bounds for the first non-zero Steklov eigenvalue

2018/02/11 by Verma, Sheela · 1 citation
#35P15 #53C20 #53C42 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.03747

Abstract

Let Ω be a star-shaped bounded domain in (\mathbbSⁿ, ds²) with smooth boundary. In this article, we give a sharp lower bound for the first non-zero eigenvalue of the Steklov eigenvalue problem in Ω. This result is the generalization of a result given by Kuttler and Sigillito for a star-shaped bounded domain in ℝ². Further we also obtain a two sided bound for the first non-zero eigenvalue of the Steklov problem on the ball in ℝⁿ with rotationally invariant metric and with bounded radial curvature.

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• Biharmonic Steklov problems with Neumann boundary conditions and spectral inequalities on differential forms

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