Spectral asymptotics for Dirichlet to Neumann operator
Victor Yakovlevich Ivrii · arXiv (Cornell University) · 2018
We consider eigenvalues of the Dirichlet-to-Neumann operator for Laplacian in the domain (or manifold) with edges and establish the asymptotics of the eigenvalue counting function \begin{equation*} \mathsf{N}(λ)= κ_0λ^d +O(λ^{d-1})\qquad \text{as}\ \ λ\to+\infty, \end{equation*} where $d$ is dimension of the boundary. Further, in certain cases we establish two-term asymptotics \begin{equation*} \mathsf{N}(λ)= κ_0λ^d+κ_1λ^{d-1}+o(λ^{d-1})\qquad \text{as}\ \ λ\to+\infty. \end{equation*} We also establish improved asymptotics for Riesz means.