Seminar

We consider the problem of unique continuation from infinity for linear waves on a curved background. We derive new Carleman estimates from infinity for wave operators on Minkowski, Schwarzschild and certain perturbations thereof, which allow us to conclude that solutions to a wave equation vanishing to infinite order on suitable portions of future and past null infinity imply that the solution itself vanishes in an open region of spacetime. Surprisingly, the result in Schwarzschild is stronger than the one in Minkowski spacetime. Moreover, we show that our results are sharp (in particular infinite order vanishing is necessary). These results are motivated by questions in General Relativity. This is joint work with Spyros Alexakis and Arick Shao.