University of Cambridge > > Partial Differential Equations seminar > Unique continuation from infinity for linear waves

Unique continuation from infinity for linear waves

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If you have a question about this talk, please contact Harsha Hutridurga.

We prove various unique continuation results from infinity for linear waves on asymptotically flat space-times. Assuming vanishing of the solution to infinite order on suitable parts of future and past null infinities, we derive that the solution must vanish in an open set in the interior. The parts of infinity where we must impose a vanishing condition depend strongly on the background geometry; in particular, for backgrounds with positive mass (such as Schwarzschild or Kerr), the required assumptions are much weaker than in Minkowski spacetime. These results rely on a new family of geometrically robust Carleman estimates near null cones and on an adaptation of the standard conformal inversion of Minkowski spacetime. Also, the results are nearly optimal in many respects.

This is joint work with Spyros Alexakis and Volker Schlue.

This talk is part of the Partial Differential Equations seminar series.

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