(untitled) (Analysis in Theory and Applications, 2025)
Let Ω be a domain with a hole containing the origin in R^2 and u be a solution to the problem where ^±Ω represents the outer and inner boundaries of Ω, respectively, c is a constant. Let μ_k denote the kth Neumann eigenvalue of the Laplacian on Ω andΩ_h is the hole. We establish that if μ< μ_8, then Ω is an annulus.