In this presentation, based on joint works with Jerome LeRousseau and Matthieu
Leautaud, we consider boundary problems forelliptic/parabolic operators.
We prove Carleman estimates in such cases. One of the interest for such
an estimate is the implied controllability of (semi-linear) heat equations.
One of the main aspects of the proof is a microlocal decomposition
separating high and low tangential frequencies. If time permits, we
will present how such an approach can be used to prove Carleman estimates
in the case of non smooth coefficients at an interface, possibly
with an additional diffusion process along the interface.
Seminar on Analysis at University of Tsukuba