A Lower Bound for the First Steklov Eigenvalue on a Domain

@inproceedings{Garca2015ALB,
  title={A Lower Bound for the First Steklov Eigenvalue on a Domain},
  author={Gonzalo Garc{\'i}a and {\'O}scar Andr{\'e}s Monta{\~n}o},
  year={2015}
}
In this paper we provide a lower bound for the first eigenvalue of the Steklov problem in a star-shaped bounded domain in Rn. This result extends to higher dimensions a lower estimate of Kuttler-Sigillito in a two dimensional star-shaped bounded domain. 

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References

SHOWING 1-7 OF 7 REFERENCES

Cota superior para el primer valor propio del problema de Steklov

Let Br be an n-dimensional ball endowed with a rotationally in- variant metric and with non-positive radial sectional curvatures. Ifis the �rst Steklov eigenvalue and h is the mean curvature on the

Bounds for Stekloff Eigenvalues

The smallest nonzero Stekloff eigenvalue $\xi _2 $ satisfying $\Delta ^2 w = 0$ in R, ${{\partial w} / {\partial n}} = {{\partial \Delta w} / {\partial n}} + \xi w = 0$ on $\partial R$, is an optimal

The Geometry of the First Non-zero Stekloff Eigenvalue

Let (Mn, g) be a compact Riemannian manifold with boundary and dimensionn⩾2. In this paper we discuss the first non-zero eigenvalue problem \begin{align}\Delta\varphi & = & 0\qquad & on\quad M,\\

Some Isoperimetric Inequalities for Harmonic Functions

Inequalities for a Classical Eigenvalue Problem

445–490 (fr). Revista Colombiana de Matemáticas i i “v49n1a05-GarciaMontano

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