Spectral asymptotics for the Dirichlet Laplacian with a Neumann window via a Birman-Schwinger analysis of the Dirichlet-to-Neumann operator

2015/11/17 by André Hänel, Hänel, André, Timo Weidl +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1511.05529

Abstract

In the present article we will give a new proof of the ground state asymptotics of the Dirichlet Laplacian with a Neumann window acting on functions which are defined on a two-dimensional infinite strip or a three-dimensional infinite layer. The proof is based on the analysis of the corresponding Dirichlet-to-Neumann operator as a first order classical pseudo-differential operator. Using the explicit representation of its symbol we prove an asymptotic expansion as the window length decreases.

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