The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials
type: Item
instance of: scholarly article
title: The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials
zbMATH Open document ID: 1372.35095
author: Jussi Behrndt
author: A. F. M. ter Elst
published in: Discrete and Continuous Dynamical Systems. Series S
publication date: 2017-05-03T00:00:00Z
review text: The paper deals with the Dirichlet-to-Neumann operator \(D\) acting on functions defined on the Lipschitz boundary \(\Gamma=\partial \Omega\) of a bounded open set \(\Omega\subset \mathbb{R}^d\), defined by \(D\varphi=\psi\), \(\text{Dom}\,D\subset L_2(\Gamma)\), \(\psi\in L_2(\Gamma)\) for which there exists a \(u\in H^1(\Omega)\) such that \[ \begin{cases} \text{Tr}\,u =\varphi,\\ -\Delta u+qu=0,\,\,\,\text{weakly on} \,\,\Omega,\\ \partial_{\nu}u=\psi, \end{cases} \] where \(\partial_{\nu}\) is the weak normal derivative, and \(q:\Omega\to \mathbb{C}\) is a bounded measurable complex valued function. The authors investigate some properties of the operator \(D\), by using form methods and the theory of self-adjoint graphs.
Mathematics Subject Classification ID: 35J57
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 6710661
zbMATH Keywords: Dirichlet-to-Neumann graph
zbMATH Keywords: \(m\)-sectorial graph
zbMATH Keywords: form methods
reviewed by: Rodica Luca
MaRDI profile type: Publication
full work available at URL: dcdss.2017033
OpenAlex ID: W2605530916
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DOI: 10.3934/DCDSS.2017033
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description: scientific article; zbMATH DE number 6710661