Mathematics > Home > Advances in Pure and Applied Mathematics > Issue 2 (September 2020) > Article
Sheela Verma
Centre For Applicable Mathematics
India
G. Santhanam
Indian Institute of Technology Kanpur
India
Published on 3 September 2020 DOI : 10.21494/ISTE.OP.2020.0544
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.
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.
Laplacian Steklov eigenvalue problem Star-shaped domain Rayleigh quotient
Laplacian Steklov eigenvalue problem Star-shaped domain Rayleigh quotient