Séminaire du CERAMATHS - DMATHS : exposé de Matthias Täufer

Le séminaire du département de mathématiques du CERAMATHS accueillera à 14h Matthias Täufer (FernUniversität in Hagen, Allemagne) lundi 1er juillet 2024, pour l'exposé suivant :

Quantitative unique continuation and applications

Unique continuation is a rigidity property which many solutions of PDEs have: If they vanish on a subdomain they cannot vanish identically. Quantitative variants of unique continuation establish a relation between the norm of functions and the norm of their restriction to a subdomain and are an exciting field connecting harmonic analysis with spectral theory and applications to engineering and Mathematical Physics.

In this talk, I will present several quantitative unique continuation estimates for functions in spectral subspaces of Schrödinger operators and two applications thereof: (1) Control cost estimates for the heat equation with explicit estimates on the cost of controllability which allow to study controllability in the so-called homogenization regime, and (2) Anderson localization for random Schrödinger operators.