Michele Di Cristo

An inverse scattering problem for a partially coated buried obstacle

We consider an inverse scattering problem for a perfect conductor that is partially coated by a dielectric. We investigate a method for determining the shape of the object from the Cauchy data of the total field measured on the boundary of a domain containing the object in its interior. We then give a variational characterization of the supremum of the surface impedance and validate the method with some numerical examples. Applications are given to the target identification of a buried partially coated perfect conductor from a knowledge of the electric and magnetic field on the surface of the earth.

Stable determination of the discontinuous conductivity coefficient of a parabolic equation

We deal with the problem of determining a time varying inclusion within a thermal conductor. In particular we study the continuous dependance of the inclusion from the Dirichlet--to--Neumann map. Under a priori regularity assumptions on the unknown defect we establish logarithmic stability estimates.

Article A Multistep Reciprocity Gap Functional Method for the Inverse Problem in a Multi-layered Medium

We introduce a multistep reciprocity gap functional method to reconstruct the support of a target embedded in a multi-layered medium from near field measurements at a fixed frequency. The approach is based on the use of the standard reciprocity gap functional method for homogeneous background to strip the layers and recover the data at each interface by means of the so-called interior transmission problem and then, at the last step, to reconstruct the support of the scatterer. The advantage of this approach is that it avoids computing the Greens function for multi-layered medium. Numerical examples are given, showing the performance of our reconstruction algorithm.

The Determination of the Support and Surface Conductivity of a Partially Coated Buried Object

We consider a partially coated anisotropic medium and determine its shape by knowledge of Cauchy data on the boundary of a domain where we a priori know that the obstacle is located. We then give a variational characterization of the supreme of the surface conductivity and validate the method with some numerical examples.

Exponential instability for inverse elliptic problems with unknown boundaries

We prove that the inverse problem of determining unknown defects of various types in a conductor by performing electrostatic measurements at the boundary is severely ill-posed. We show that the ill-posedness does not depend on the nature of the defects to be determined and, more importantly, by the kind, choice and number of measurements performed.

Size estimates of unknown boundaries with a Robin-type condition

We deal with the problem of determining an unknown part of the boundary of an electrical conductor that is not accessible from an external observation and where a corrosion process is going on. We obtain estimates from above and below of the size of this damaged region.