– Europe/Lisbon
Room 6.2.38, Faculty of Sciences of the Universidade de Lisboa — Online

Didier Pilod, University of Bergen
On the fractional Schrödinger equation with variable coefficients
We study the initial value problem (IVP) associated with the semi-linear fractional Schrödinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modeling the dispersion relation and use them to establish the local well-posedness for the corresponding IVP. Also, we obtain unique continuation results concerning the solutions of this problem. These are consequences of uniqueness properties that we prove for the fractional elliptic operator with variable coefficients.
This talk is based on a joint work with C. Kenig (Chicago), G. Ponce (Santa Barbara), and L. Vega (Bilbao).