https://sites.google.com/view/garciaferrero
Thu, December 1, 2022, 9:00-10:00 am PDT via Zoom
Title: The Calderón problem for directionally antilocal operators.
Abstract:
The Calderón problem for the fractional Schrödinger equation, introduced by T. Ghosh, M. Salo and G. Uhlmann, satisfies global uniqueness with only one single measurement. This result exploits the antilocality property of the fractional Laplacian, that is, if a function and its fractional Laplacian vanish in a subset, then the function is zero everywhere.
Nonlocal operators which only depend on the function in some directions and not on the whole space cannot satisfy an analogous antilocality property. In theses cases, only directional antilocality conditions may be expected.
In this talk, we will consider antilocality in cones, introduced by Y. Ishikawa in the 80s, and its possible implications in the corresponding Calderón problem. In particular, we will see that uniqueness for the associated Calderón problem holds even with a singe measurement, but new geometric conditions are required.
This is a joint work with G. Covi and A. Rüland.