5 papers · 1 filter
Resolvent bounds imply observability from measurable time sets for Schrödinger equations
Nicolas Burq, Hui Zhu
We prove that on a compact Riemannian manifold, resolvent bounds for the Laplace--Beltrami operator imply observability, and thus controllability, for the Schrödinger propagator f…
Observability of Schrödinger propagators on tori in rough settings
Nicolas Burq, Hui Zhu
On tori of arbitrary dimensions, Schrödinger propagators with bounded potentials are conjectured to be observable from space-time domains of positive Lebesgue measure. We reduce t…
Trace and Observability Inequalities for Laplace Eigenfunctions on the Torus
Nicolas Burq, Pierre Germain, Massimo Sorella +1
We investigate trace and observability inequalities for Laplace eigenfunctions on the d-dimensional torus, with respect to arbitrary Borel measures . Specifically, we character…
Measure and continuous vector field at a boundary II: geodesics and support propagation
Nicolas Burq, Belhassen Dehman, Jérôme Le Rousseau
Nonnegative measures that are solutions to a transport equation with continuous coefficients have been widely studied. Because of the low regularity of the associated vector field,…
Measure and continuous vector field at a boundary I: propagation equations and wave observability
Nicolas Burq, Belhassen Dehman, Jérôme Le Rousseau
The celebrated geometric control condition of Bardos, Lebeau, and Rauch is necessary and sufficient for wave observability [1,7] and exact controllability. It requires that any poi…