@ARTICLE{10.21494/ISTE.OP.2020.0544, 

TITLE={Sharp bounds for Steklov eigenvalues on star-shaped domains}, 
  
AUTHOR={Sheela Verma, G. Santhanam, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={11}, 

NUMBER={Issue 2 (September 2020)}, 
	
YEAR={2020}, 

URL={https://openscience.fr/Sharp-bounds-for-Steklov-eigenvalues-on-star-shaped-domains}, 
	
DOI={10.21494/ISTE.OP.2020.0544}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={In this article, we consider Steklov eigenvalue problem on star-shaped bounded domain Ω in hypersurface of revolution and paraboloid, P = {(x, y, z) ∈ ℝ3 : z = x2 + y2}. A sharp lower bound is derived for all Steklov eigenvalues of Ω in terms of the Steklov eigenvalues of the largest geodesic ball contained in Ω with the same center as Ω. This work is a generalization of a result given by Kuttler and Sigillito (SIAM Rev 10:368 − 370, 1968) on a star-shaped bounded domain in ℝ2.}}