Eigenvalue estimates on domain of the polydisk

In this paper, we investigate universal inequalities for eigenvalues of the Dirichlet Laplacian and the clamped plate problem on a bounded domain in an n-dimensional polydisk D ⁿ. Moreover, from the domain monotonicity of the eigenvalue, we can prove that if the first eigenvalue of the Dirichlet Laplacian tends to n/4 when the domain tends to the polydisk D ⁿ, then all of the eigenvalues tend to n/4.