On the Eigenvalues of the Biharmonic Steklov Problem on a Thin Set

Abstract

This paper investigates the asymptotic behavior of the eigenvalues of the biharmonic operator on a thin set with Steklov boundary condition. The thin set is taken to be a tubular neighborhood of a planar smooth domain. We show that, as the thickness of this neighborhood tends to zero, all eigenvalues of the biharmonic operator with Steklov boundary condition converge to zero.

Submitted to Math. Methods Appl. Sci