Boundary distance: volume and geodesic ray transform
Seminar Room 2, Newton Institute Gatehouse
AbstractIn dimension 2 the best avalaible result is due to Astala and Päivärinta. They were able to combine the approach based on the scattering transform introduced by Nachman with the theory of quasiconformal maps to show that, in any planar domain, any function essentially bounded from above and below could be identified by boundary measurements.
In the talk we will show that if the oscillation of the conductivities is controlled in some fractional Sobolev space and the boundary of the domain has Minkowski dimension less than 2 the identification is stable. We will also discuss the relation between the concept of G-convergence and Dirichlet to Neuman maps to show the sharpness of the result.