Carleman Estimates and Some Applications to Control Theory

摘要

We prove Carleman estimates for elliptic and parabolic operators,using several methods: a microlocal approach where the main tool is the G?rding inequality and a more computational direct approach. Carleman estimates are proven locally and we describe how they can be patched together to form a global estimate. We expose how they can be used to provide unique continuation properties,as well as approximate and null controllability results.