The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials

Jussi Behrndt; A. F. M. ter Elst

doi:10.3934/dcdss.2017033

Article Contents

2017, Volume 10, Issue 4: 661-671. Doi: 10.3934/dcdss.2017033

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The Dirichlet-to-Neumann map for Schrödinger operators with complex potentials

Jussi Behrndt^1, and
A. F. M. ter Elst^2, ,

1.
Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010 Graz, Austria
2.
Department of Mathematics, University of Auckland, Private bag 92019, Auckland 1142, New Zealand

^* Corresponding author: A.F.M ter Elst
^* Corresponding author: A.F.M ter Elst

Received: May 31, 2016

Revised: November 30, 2016

Published: July 2017

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Abstract

Let $\Omega \subset \mathbb{R}^d$ be a bounded open set with Lipschitz boundary and let $q \colon \Omega \to \mathbb{C}$ be a bounded complex potential. We study the Dirichlet-to-Neumann graph associated with the operator $- \Delta + q$ and we give an example in which it is not $m$-sectorial.

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Mathematics Subject Classification: 35J57, 47F05.

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