4 papers
Timelike curves: homotopies and domain of determinacy
Jérôme Le Rousseau, Jeffrey B. Rauch
This paper studies domains of determination of linear strictly hyperbolic second order operators . For an open set , a set is a domain of determination when the…
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…