Bounds for the first non-zero Steklov eigenvalue

Sheela Verma

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arXiv · 1802.03747

Bounds for the first non-zero Steklov eigenvalue

Sheela Verma

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Abstract

Let $\Omega$ be a star-shaped bounded domain in $(\mathbb{S}^{n}, ds^{2})$ with smooth boundary. In this article, we give a sharp lower bound for the first non-zero eigenvalue of the Steklov eigenvalue problem in $\Omega.$ This result is the generalization of a result given by Kuttler and Sigillito for a star-shaped bounded domain in $\mathbb{R}^2.$ Further we also obtain a two sided bound for the first non-zero eigenvalue of the Steklov problem on the ball in $\mathbb{R}^n$ with rotationally invariant metric and with bounded radial curvature.

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BibTeX RIS

Sheela Verma. 2018-02-11. Bounds for the first non-zero Steklov eigenvalue. https://arxiv.org/abs/1802.03747

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