Stability for the Gel'fand inverse problem

Inverse Problems and Applications

11 March 15:30 - 16:30


We study anisotropic Multidimensional Inverse Problems (MIP) for partial differential equations on manifolds. A distinguishing feature of anisotropic MIP is the non-uniqueness as a result of the coordinate and gauge invariance of boundary measurements. For this reason we study MIP on manifolds, avoiding difficulties due to a specific choice of coordinates. The Gel'fand inverse boundary spectral problem is related to the questions: 1. Do the boundary spectral data determine (M,g)? 2. And do a finite set of these data determine an approximation of (M,g) in a stable way? A classical method of stabilizing inverse problems is to identify some proper compact sets in the class of Riemannian manifolds. This is related to Cheeger-Gromov theory of geometric convergence, which makes it possible to formulate the desired conditions in terms of diameter, curvature and other geometric constraints. We will discuss these questions on the basis of the work by [Y. Kurylev, & coauthors] and some recent results.