The interior transmission problem

By David Colton, Lassi PÄIVÄRINTA #, John Sylvester. 2007

230 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e16eaccd76d5d39b8c920c152d7830f48c1fdbc

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In Biomedical Engineering

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On the use of T-coercivity to study the interior transmission eigenvalue problem (2011, background): “Indeed, the equivalent formulation of problem (3) we consider, which presents a useful property of positivity, is no longer symmetric: that prevents using the classical min-max arguments (see [4,6]).”
On the existence of transmission eigenvalues (2009, background): “The recent survey paper [7] reports on the state of the art for the interior transmission problems till the end of 2007.”
Analytical and computational methods for transmission eigenvalues (2010, background): “As opposed to previous estimates obtained via Faber-Krahn type inequalities [13, 5], these bounds are clearly sharp for n(x) equal to a constant and D a ball.”