Inverse Problems and Imaging (IPI)

The interior transmission problem

Pages: 13 - 28, Volume 1, Issue 1, February 2007      doi:10.3934/ipi.2007.1.13

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David Colton - Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, United States (email)
Lassi Päivärinta - Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FI-00014, Finland (email)
John Sylvester - Department of Mathematics, University of Washington, Seattle, Washington 98195, United States (email)

Abstract: The interior transmission problem is a boundary value problem that plays a basic role in inverse scattering theory but unfortunately does not seem to be included in any existing theory in partial differential equations.This paper presents old and new results for the interior transmission problem ,in particular its relation to inverse scattering theory and new results on the spectral theory associated with this class of boundary value problems.

Keywords:   Interior Transmission Problem.
Mathematics Subject Classification:  Primary: 81U40, 35P25.

Received: July 2006;      Revised: October 2006;      Available Online: January 2007.