The unique continuation property is a fundamental concept in the field of partial differential equations, which describes propagation of the zeros of solutions to PDEs. Essentially, it asks what condition is required to guarantee that if a solution to a PDE vanishes on a certain subset of the spatial domain, then it must also vanish on a larger subset of the domain.
In a series of papers by Escauriaza, Kenig, Ponce and Vega, motivated by Hardy's uncertainty principle, they were able to asked the question from a different perspective. That is, they showed that if a linear Schr\”odinger solution decays sufficiently fast at two different times, the solution must be trivial. In this talk, we will discuss unique continuation properties of solutions to higherorder Schr\"odinger equations and variablecoefficient Schr\”odinger equations, and extend the classical EscauriazaKenigPonceVega type of result to these models. This is based on joint works with S. Federico Z. Li, and Z. Lee.
Some unique continuation results for Schrodinger equations
Xueying Yu, University of Washington

SMI 307