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### Open Access Journals

IPI

The interior transmission problem plays a basic role in the study of
inverse scattering problems for inhomogeneous medium. In this paper
we study the interior transmission problem for the Maxwell equations
in the electromagnetic scattering problem for an anisotropic
inhomogeneous object. We use a variational approach which extends
the method developed in [15] to the case when the index of
refraction is less than one as well as for partially coated
scatterers. In addition, we also describe the structure of the
transmission eigenvalues.

IPI

We use the Factorization method to retrieve the shape of cracks with impedance
boundary conditions from farfields associated with incident plane waves at a
fixed frequency. This work is an extension of the study initiated by Kirsch and
Ritter [Inverse Problems, 16, pp. 89-105, 2000]
where the case of sound soft cracks is considered. We address here the scalar
problem and provide theoretical validation of the method when the impedance boundary
conditions hold on both sides of the crack. We then deduce an inversion
algorithm and present some validating numerical results in the case of simply
and multiply connected cracks.

IPI

In the context of scattering problems in the harmonic regime, we consider the problem of
identification of some Generalized Impedance Boundary Conditions (GIBC) at the
boundary of an object (which is supposed to be known) from far field
measurements associated with
a single incident plane wave at a fixed frequency. The GIBCs can be seen as approximate
models
for thin coatings, corrugated surfaces or highly absorbing media.
After pointing out that uniqueness does not hold in the general case, we propose some
additional assumptions for which uniqueness can be restored.
We also consider the question of stability when uniqueness holds. We prove in
particular Lipschitz stability when the impedance parameters belong to a
compact subset of a finite dimensional space.

IPI

We consider the interior transmission problem corresponding to the inverse scattering by an inhomogeneous (possibly anisotropic) media in which an impenetrable obstacle with Dirichlet boundary conditions is embedded. Our main focus is to understand the associated eigenvalue problem, more specifically to prove that the transmission eigenvalues form a discrete set and show that they exist. The presence of Dirichlet obstacle brings new difficulties to already complicated situation dealing with a non-selfadjoint eigenvalue problem. In this paper, we employ a variety of variational techniques under various assumptions on the index of refraction as well as the size of the Dirichlet obstacle.

IPI

This special issue is dedicated to Professors David Colton and
Rainer Kress in honor of their contribution and leadership in the
area of direct and inverse scattering theory for more then 30
years. The papers in this special issue were solicited from the
invited speakers at the International Conference on Inverse
Scattering Problems organized in honor of the 65th birthdays of
David Colton and Rainer Kress held in the seaside resort of Sestry
Levante, Italy, May 8-10, 2008.

As organizers of this conference and close collaborators of Professors Colton and Kress, we are very honored to have had the opportunity to facilitate this special scientific and social event. It was a particular occasion that gathered together long term colleagues, collaborators, former students and friends of Professors Colton and Kress. And now it gives us particular pleasure to be guest editors of this special issue of Inverse Problems and Imaging which is a collection of original research papers in the area of scattering theory and inverse problems. Much of the work presented here has been directly or indirectly influenced by these two scientists, offering the reader a glimpse of their significant impact in this research area.

We would like to thank all of those who have contributed a paper for this special issue. A special thanks goes to the Editor in Chief of Inverse Problems and Imaging, Lassi Päivärinta, for supporting and facilitating this publication. We would also like to thank all the participants of the Sestri Levante Conference who made such a successful, stimulating and pleasant event possible. Last (but definitely not least!) we would like to thank the sponsors of the conference: the European Office of Aerospace Research and Development of the United States Air Force Office of Scientific Research, the University of Genova, the University of Verona, the Istituto Nazionale di Alta Matematica - Gruppo Nazionale di Calcolo Scientifico, the University of Göttingen, the University of Delaware and INRIA Center of Saclay Ile de France.

As organizers of this conference and close collaborators of Professors Colton and Kress, we are very honored to have had the opportunity to facilitate this special scientific and social event. It was a particular occasion that gathered together long term colleagues, collaborators, former students and friends of Professors Colton and Kress. And now it gives us particular pleasure to be guest editors of this special issue of Inverse Problems and Imaging which is a collection of original research papers in the area of scattering theory and inverse problems. Much of the work presented here has been directly or indirectly influenced by these two scientists, offering the reader a glimpse of their significant impact in this research area.

We would like to thank all of those who have contributed a paper for this special issue. A special thanks goes to the Editor in Chief of Inverse Problems and Imaging, Lassi Päivärinta, for supporting and facilitating this publication. We would also like to thank all the participants of the Sestri Levante Conference who made such a successful, stimulating and pleasant event possible. Last (but definitely not least!) we would like to thank the sponsors of the conference: the European Office of Aerospace Research and Development of the United States Air Force Office of Scientific Research, the University of Genova, the University of Verona, the Istituto Nazionale di Alta Matematica - Gruppo Nazionale di Calcolo Scientifico, the University of Göttingen, the University of Delaware and INRIA Center of Saclay Ile de France.

keywords:

IPI

We present a new qualitative imaging method capable of selecting defects in
complex and unknown background from differential measurements of farfield
operators: i.e. far measurements of scattered waves in the cases with and
without defects. Indeed, the main difficulty is that the background physical
properties are unknown. Our approach is based on a new exact characterization
of a scatterer domain in terms of the far field operator range and the link
with solutions to so-called interior transmission problems. We present the
theoretical foundations of the method and some validating numerical experiments
in a two dimensional setting.

## Year of publication

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