Keith Rogers (Instituto de Ciencias Matemáticas)

Title: On control of sobolev norms with localized data

Abstract: We will consider the inverse scattering problem at a fixed energy in the plane. That is to recover a potential from the scattered plane waves with a fixed frequency, incoming from all directions and then measured in all@directions. We will provide explicit formulae with which one can recover@compactly supported potentials with half a derivative in L2, and show that below this level of regularity the recovery process can fail.@This is joint work with Kari Astala and Daniel Faraco.