## Bounds for the first non-zero Steklov eigenvalue. (arXiv:1802.03747v1 [math.DG])

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.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 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.