Seminario EDPs y Mecánica de Fluidos

Carleman estimates for parabolic operators with potentials diverging as an inverse square on a hypersurface

Ponente:  Bruno Vergara (Universitat de Barcelona)
Fecha:  martes 16 de noviembre de 2021 - 12:00
Lugar:  Aula Azul (ICMAT)


In this talk I will discuss new quantitative uniqueness results on parabolic equations with singular potentials diverging as an inverse square of the distance to a hypersurface in \(\mathbb{R}^n\). Using Carleman inequalities techniques, we establish estimates that are sharp in the sense that they capture both the natural energy and boundary conditions for the problem. In particular, I will describe the role of the hypersurface geometry in the proof of our estimates and discuss its relationship with the range of the strength potential parameter. Applications including boundary control, observability and unique continuation will be shown too. This is joint work with Alberto Enciso and Arick Shao.