Bounds on positive interior transmission eigenvalues

The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds justify the existence of an infinite set of interior transmission eigenvalues and provide asymptotic estimates from above on the counting function for the large values of the wave number. They also lead to certain important upper estimates on the first few interior transmission eigenvalues. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle.Comment: We corrected inaccuracies cost by the wrong sign in the Green formula (17). In particular, the sign in the definition of \sigma was change

Reconstruction of discontinuous parameters in a second order impedance boundary operator

International audienceWe consider the inverse problem of retrieving the coefficients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the differentiability of the Khon-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of unknown number of discontinuity points

A NEW LINEAR SAMPLING METHOD FOR THE ELECTROMAGNETIC IMAGINING OF BURIED OBJECTS

We present a new linear sampling method for determining the shape of scattering objects imbedded in a known inhomogeneous medium from a knowledge of the scattered electromagnetic field due to a point source incident field at fixed frequency. The method does not require any a prior information on the physical properties of the scattering object and, under some restrictions, avoids the need to compute the Green’s tensor for the background medium. 1