Results 1  10
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16
The interior transmission problem
 Inverse Probl. Imaging
"... 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 p ..."
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Cited by 48 (13 self)
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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. 1.
The inverse electromagnetic scattering problem for a partially coated dielectric
 J. Comp. Appl. Math
"... Abstract. The inverse electromagnetic scattering problem for anisotropic media plays a special role in inverse scattering theory due to the fact that the (matrix) index of refraction is not uniquely determined from the far field pattern of the scattered field even if multifrequency data is availabl ..."
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Cited by 20 (10 self)
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Abstract. The inverse electromagnetic scattering problem for anisotropic media plays a special role in inverse scattering theory due to the fact that the (matrix) index of refraction is not uniquely determined from the far field pattern of the scattered field even if multifrequency data is available. In this paper we describe how transmission eigenvalues can be determined from the far field pattern and be used to obtain upper and lower bounds on the norm of the index of refraction. Numerical examples will be given for the case when the scattering object is an infinite cylinder and the inhomogeneous medium is orthotropic. 1.
The computation of lower bounds for the norm of the index of refraction in an anisotropic media from far field data
 Jour. Integral Equations and Applications
"... Dedicated to Professor Dr. Rainer Kress on the occasion of his 65th birthday and the pleasure that knowing him has given to our lives! ABSTRACT. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under cert ..."
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Cited by 19 (8 self)
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Dedicated to Professor Dr. Rainer Kress on the occasion of his 65th birthday and the pleasure that knowing him has given to our lives! ABSTRACT. We consider the scattering of time harmonic electromagnetic plane waves by a bounded, inhomogeneous, anisotropic dielectric medium and show that under certain assumptions a lower bound on the norm of the (matrix) index of refraction can be obtained from a knowledge of the smallest transmission eigenvalue corresponding to the medium. Numerical examples are given showing the efficaciousness of our estimates. 1. Introduction. Anisotropic
The determination of the surface conductivity of a partially coated dielectric
 SIAM J. Appl. Math
"... Abstract. A variational method is given for determining the essential supremum of the surface conductivity of a partially coated anisotropic dielectric medium from a knowledge of the far field pattern of the timeharmonic electric field at fixed frequency corresponding to an incident plane wave. It ..."
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Cited by 19 (9 self)
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Abstract. A variational method is given for determining the essential supremum of the surface conductivity of a partially coated anisotropic dielectric medium from a knowledge of the far field pattern of the timeharmonic electric field at fixed frequency corresponding to an incident plane wave. It is assumed that the shape of the scatterer has been determined (e.g., by solving the far field equation and using the linear sampling method). Numerical examples are given for the scalar case with constant surface conductivity.
A variational approach for the solution of the electromagnetic interior transmission problem for anisotropic media, Inverse Problems and Imaging 1
, 2007
"... (Communicated by David Colton) Abstract. 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 anis ..."
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Cited by 15 (8 self)
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(Communicated by David Colton) Abstract. 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. 1.
Open problems in the qualitative approach to inverse electromagnetic scattering theory
 European Jour. Applied Math
"... We formulate a number of open problems for timeharmonic inverse electromagnetic scattering theory focusing on uniqueness theorems, the determination of the support of a scattering object and the determination of material parameters 1 ..."
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Cited by 5 (2 self)
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We formulate a number of open problems for timeharmonic inverse electromagnetic scattering theory focusing on uniqueness theorems, the determination of the support of a scattering object and the determination of material parameters 1
A target signature for distinguishing perfect conductors from anisotropic media of finite conductivity
 Math. Comput. Simulation
"... of finite conductivity ..."
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U.S.A.
, 2006
"... The interior transmission problem is a boundary value problem arising in inverse scattering theory that, to our knowledge, is not covered by any existing theory in partial differential equations. Nevertheless, the problem is easy to state and a better understanding of conditions under which this pr ..."
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The interior transmission problem is a boundary value problem arising in inverse scattering theory that, to our knowledge, is not covered by any existing theory in partial differential equations. Nevertheless, the problem is easy to state and a better understanding of conditions under which this problem is
THE INVERSE SCATTERING PROBLEM FOR ANISOTROPIC MEDIA
"... We give a survey of recent results on the inverse scattering problem for anisotropic media including both uniqueness theorems and reconstruction algorithms. 1. ..."
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We give a survey of recent results on the inverse scattering problem for anisotropic media including both uniqueness theorems and reconstruction algorithms. 1.