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