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• W2964145118 abstract "This paper studies eigenvalues of some Steklov problems. Among other things, we show the following sharp estimates. Let Ω be a bounded smooth domain in an n(⩾2)-dimensional Hadamard manifold an let 0 = λ0 < λ1 ⩽ λ2 ⩽ … denote the eigenvalues of the Steklov problem: Δu = 0 in Ω and (∂u)/(∂ν) = λu on ∂Ω. Then ∑i=1nλi-1⩾(n2|Ω|)/(|∂Ω|) with equality holding if and only if Ω is isometric to an n-dimensional Euclidean ball. Let M be an n(⩾ 2)-dimensional compact connected Riemannian manifold with boundary and non-negative Ricci curvature. Assume that the mean curvature of ∂M is bounded below by a positive constant c and let q1 be the first eigenvalue of the Steklov problem: Δ2u = 0 in M and u = (∂2u)/(∂ν2) − q(∂ u)/(∂ν) = 0 on ∂M. Then q1 ⩾ c with equality holding if and only if M is isometric to a ball of radius 1/c in Rn." @default.
• W2964145118 created "2019-07-30" @default.
• W2964145118 creator A5012302576 @default.
• W2964145118 creator A5024736790 @default.
• W2964145118 date "2013-03-01" @default.
• W2964145118 modified "2023-09-23" @default.
• W2964145118 title "Inequalities for the Steklov eigenvalues" @default.
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• W2964145118 doi "https://doi.org/10.1016/j.chaos.2013.01.008" @default.
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