Control of waves on Lorentzian manifolds with curvature bounds

Abstract

We prove boundary controllability results for wave equations (with lower-order terms) on Lorentzian manifolds with time-dependent geometry satisfying suitable curvature bounds. The main ingredient is a novel global Carleman estimate on Lorentzian manifolds that is supported in the exterior of a null (or characteristic) cone, which leads to both an observability inequality and bounds for the corresponding constant. The Carleman estimate also yields a unique continuation result on the null cone exterior, which has applications toward inverse problems for linear waves on Lorentzian backgrounds.

arXiv comment55 pages

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• Null Geodesics and Improved Unique Continuation for Waves in Asymptotically Anti-de Sitter Spacetimes
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