Homogenization of Steklov eigenvalues with rapidly oscillating weights

Abstract

In this article we study the homogenization rates of eigenvalues of a Steklov problem with rapidly oscillating periodic weight functions. The results are obtained via a careful study of oscillating functions on the boundary and a precise estimate of the $L^{\infty }$ bound of eigenfunctions. As an application we provide some estimates on the first nontrivial curve of the Dancer-{F}u{č}{\'ı}k spectrum.

19 pages