# American Institute of Mathematical Sciences

February  2007, 1(1): 13-28. doi: 10.3934/ipi.2007.1.13

## The interior transmission problem

 1 Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, United States 2 Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FI-00014 3 Department of Mathematics, University of Washington, Seattle, Washington 98195, United States

Received  July 2006 Revised  October 2006 Published  January 2007

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.
Citation: David Colton, Lassi Päivärinta, John Sylvester. The interior transmission problem. Inverse Problems and Imaging, 2007, 1 (1) : 13-28. doi: 10.3934/ipi.2007.1.13
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