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

## Lili_Yan.jpg

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.

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