4 papers
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…
Semi-classical analysis
Clotilde Fermanian Kammerer, Jérôme Le Rousseau
We introduce three representative topics in semi-classical analysis. Starting from the correspondence between classical and quantum mechanics, basic semi-classical analysis tools a…
Semi-classical observation suffices for observability: wave and Schrödinger equations
Nicolas Burq, Belhassen Dehman, Jérôme Le Rousseau
For the wave and the Schrödinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.