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Boundary distance: volume and geodesic ray transform

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If you have a question about this talk, please contact Mustapha Amrani.

Inverse Problems

In dimension 2 the best avalaible result is due to Astala and Pivrinta. 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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