This paper considers an inverse potential problem which seeks to recover the shape of an obstacle separating two different densities by measurements of the potential. A representation for the domain derivative of the corresponding operator is established and this allows the investigation of several iterative methods for the solution of this ill-posed problem.

We are concerned with inverse obstacle scattering problems. For a fixed incident wave we consider the operator mapping an obstacle onto the far-field pattern of the scattered wave. The existence and characterizations of the Frechet derivatives for the exterior Robin problem and the transmission problem are proved.

An approach is given to extract parameters affecting phonation based upon digital high-speed recordings of vocal fold vibrations and a biomechanical model. The main parameters which affect oscillation are vibrating masses, vocal fold tension, and subglottal air pressure. By combining digital high-speed observations with the two-mass-model by Ishizaka and Flanagan (1972) as modified by Steinecke and Herzel (1995), an inversion procedure has been developed which allows the identification and quantization of laryngeal asymmetries. The problem is regarded as an optimization procedure with a nonconvex objective function. For this kind of problem, the choice of appropriate initial values is important. This optimization procedure is based on spectral features of vocal fold movements. The applicability of the inversion procedure is first demonstrated in simulated vocal fold curves. Then, inversion results are presented for a healthy voice and a hoarse voice as a case of functional dysphonia caused by laryngeal asymmetry.

This paper is devoted to the inverse scattering problem to recover a periodic structure by scattered waves measured above the structure. It is shown that a finite number of incident plane waves is sufficient to identify the structure. Additionally by a monotonicity principle for the eigenvalues of the Laplacian some upper bounds of the required number of wavenumbers are presented if a priori information on the height of the structure is available.

We consider the determination of the interior domain D ⊂ where D is characterized by a different conductivity from the surrounding medium. This amounts to solving the inverse problem of recovering the piecewise constant conductivity a = 1 + χ D in div(a∇u) = 0 from boundary data consisting of Cauchy data on the boundary of the exterior domain . We will compute the derivative of the map from the domain D to this data and use this to obtain both qualitative and quantitative measures of the solution of the inverse problem.