Differences Between Robin and Neumann Eigenvalues

Abstract

Let Ω ⊂ R2 be a bounded planar domain, with piecewise smooth boundary ∂Ω. For σ> 0 , we consider the Robin boundary value problem -Δf=λf,∂f∂n+σf=0on∂Ωwhere ∂f∂n is the derivative in the direction of the outward pointing normal to ∂Ω. Let 0