Light PhD Seminar: Stable determination of a second order perturbation of the polyharmonic operator by boundary measurements

Title
Self-improving properties of generalized Poincaré inequalities

Abstract
The inverse problem for the elliptic equation finds applications in many fields such as medical imaging, geophysics, theory of elasticity, etc. In this talk, I will discuss the inverse problem for the polyharmonic operator. We prove that the second order perturbations of the polyharmonic operator are uniquely determined by the corresponding Dirichlet to Neumann map. More precisely, we show in dimension n ≥ 3, a logarithmic type stability estimate for the inverse problem under consideration.

This is a joint work with Prof. Mourad Bellassoued.