Skip to main content

Mathematical Sciences, Analysis and PDE Seminar "Inverse boundary problems for biharmonic operators and nonlinear PDEs on the manifolds". Lili Yan, University of California Irvine

Thursday, January 20, 2022
11:00 am to 11:50 am
Floor/Room #: 
Via Zoom

Mathematical Sciences Analysis and PDE Seminar

Speaker: Lili Yan, University of California Irvine

Thursday, January 20, 2022

11:00 am - 11:50 am

Zoom Meeting ID: 958 6860 3695

Title: Inverse boundary problems for biharmonic operators and nonlinear PDEs on the manifolds

Abstract: In this talk, we consider inverse boundary value problems for biharmonic operators and nonlinear magnetic Schrodinger operators. The first result is a global uniqueness result for an inverse boundary problem for a first-order perturbation of the biharmonic operator on a conformally transversally anisotropic (CTA) Riemannian manifold of dimension $n \leq 3$. Our second result gives a constructive counterpart for it. We showed that a continuous potential can be constructively determined from the knowledge of the Dirichlet--to--Neumann map for the perturbed biharmonic operator. We also discuss the inverse boundary problem for nonlinear magnetic Schrodinger operators on a compact complex manifold.

DEPARTMENT(S):