Modul: MAT675 PDE and Mathematical Physics

## Carleman estimates and boundary observability for waves with critically singular potentials

Bruno Vergara talk

Speaker invited by: Prof. Dr. Xavier Ros-Oton

**Date:** 23.05.19 **Time:** 14.00 - 15.00 **Room:** Y27H12

In this talk I will present a novel family of Carleman inequalities on cylindrical spacetime domains featuring a potential that is critically singular, diverging as the inverse square of the distance to the boundary. These estimates, which we prove using geometric multiplier arguments that generalize the classical Morawetz inequality, are sharp in the sense that they capture both the natural boundary conditions and the natural $H^1$-energy. Quantitative uniqueness properties such as the boundary observability for the associated wave equations and parabolic analogues of the estimates will be discussed as well. This is based on joint work with A. Enciso and A. Shao.