Eva Sincich

Lipschitz stability for the inverse Robin problem

We are concerned with a problem arising in corrosion detection. We consider the stability issue for the inverse problem of determining a Robin coefficient on the inaccessible portion of the boundary by the electrostatic measurements performed on the accessible one. We provide a Lipschitz stability estimate under the further a priori assumption of a piecewise constant Robin coefficient. Furthermore, we prove that the Lipschitz constant of the above-mentioned estimate behaves exponentially with respect to the number of the portions considered.

Detecting nonlinear corrosion by electrostatic measurements

We deal with an inverse problem arising in corrosion detection. We prove a stability estimate for a nonlinear term on the inaccessible portion of the boundary by electrostatic boundary measurements on the accessible one.

Stable determination of the surface impedance of an obstacle by far field measurements

We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.

STABILITY FOR THE DETERMINATION OF UNKNOWN BOUNDARY AND IMPEDANCE WITH A ROBIN BOUNDARY CONDITION

We consider an inverse problem arising in corrosion detection. We prove a stability result of logarithmic type for the determination of the corroded portion of the boundary and impedance by two measurements on the accessible portion of the boundary.

A parabolic inverse problem with mixed boundary data. Stability estimates for the unknown boundary and impedance

We consider the problem of determining an unaccessible part of the boundary of a conductor by mean of thermal measurements. We study a problem of corrosion where a Robin type condition is prescribed on the damaged part and we prove logarithmic stability estimate.

Stable determination of surface impedance on a rough obstacle by far field data

We treat the stability of determining the boundary impedance of an obstacle by scattering data, with a single incident field. A previous result by Sincich (SIAM J. Math. Anal. 38, (2006), 434-451) showed a log stability when the boundary of the obstacle is assumed to be

Natural linearization for corrosion identification

C^{1,1}

Wave equation with Robin condition, quantitative estimates of strong unique continuation at the boundary

-smooth. We prove that, when the obstacle boundary is merely Lipschitz, a log-log type stability still holds.

Lipschitz stability for the electrostatic inverse boundary value problem with piecewise linear conductivities

We consider the numerical solution of a nonlinear problem arising in nondestructive detection of a corrosion at a hidden surface of a conductor. The problem can be naturally linearized and reduced to an elliptic Cauchy problem. In this paper we describe and test a regularized reconstruction algorithm based on a regularization by discretization, where the discretization level is chosen in data driven way.

Size estimates of unknown boundaries with a Robin-type condition

The main result of the present paper consists in a quantitative estimate of unique continuation at the boundary for solutions to the wave equation. Such estimate is the sharp quantitative counterpart of the following strong unique continuation property: let