On the fractional Schrödinger equation with variable coefficients

Speaker: Didier Pilod, Associate Professor @ UiB

Abstract: 

We study the initial value problem (IVP) associated to the semi-linear fractional Schödinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modelling 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 fractional elliptic operators with variable coefficients.

The talk is based on a joint work with Carlos Kenig (Chicago), Gustavo Ponce (Santa Barbara) and Luis Vega (Bilbao)