Thu, June 13, 2024, 9:00-10:00 am PST via Zoom
Title: Reconstruction for the Calderón problem with Lipschitz conductivities.
Abstract: I will present a reconstruction algorithm for the conductivity of the interior a body in terms of the voltage-to-current measurements on its surface. We will only assume that the conductivity is bounded above and below by positive constants and that the conductivity and surface are Lipschitz continuous. As usual, the main reconstruction formula involves a boundary integral identity which necessitates the identification of certain solutions (CGOs) on the boundary. For this, we solve the associated integral equation locally, finding solutions in $H^1(B)$, where $B$ is a ball that properly contains the body. A key ingredient is to equip this Sobolev space with an equivalent norm, depending on the complex CGO parameter as well as a real parameter associated to a Carleman estimate. The real parameter can then be chosen to yield a contraction. This is joint work with Pedro Caro and María Ángeles García-Ferrero.