Ziqi Sun

Recovery of singularities for formally determined inverse problems

In this paper we considered several formally determined problems in two dimensions. There are no global identifiability results for these problems. However, we can recover an important feature of these functions, namely their singularities. More precisely, we prove that one can determine the location and strength of singularities of anL∞ compactly supported potential by knowing the associated scattering amplitude at a fixed energy. Also we prove that one can determine the location and strength of the singularities of the sound speed of a medium by making measurements just on the boundary of the medium.

Stability estimates for hyperbolic inverse problems with local boundary data

The authors obtain stability estimates of recovery of two coefficients of a hyperbolic partial differential equation from all possible measurements implemented at a part of the lateral boundary. These estimates are of logarithmic type in the plane case and of Holder type in the three-dimensional case. As an important auxiliary result they have proved stability estimates in (attenuated) integral geometry with incomplete data.

Anisotropic inverse problems in two dimensions

Let g be a Riemannian metric on a bounded domain in two dimensions with a Lipschitz boundary. We show that one can determine the equivalent class of g and ? in the W1,p topology, 2

Electrical impedance tomography in nonlinear media

>p > 2, from knowledge of the associated Dirichlet-to-Neumann (DN) map ?g,? to the elliptic equation divg(??gu) = 0. The DN map encodes all the voltage and current measurements at the boundary.

Global identifiability for an inverse problem for the Schrödinger equation in a magnetic field.

© Journées Équations aux dérivées partielles, 1996, tous droits réservés. L’accès aux archives de la revue « Journées Équations aux dérivées partielles » (http://www. math.sciences.univ-nantes.fr/edpa/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.