Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds

2021/09/16 by Lili Yan, Yan, Lili
Computer Science · Mathematics · #35R01 #35R30 #53C65 #58J32 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2109.07712

openalex publication_date 2021/09/16 · openalex created_date 2022/12/18 · openalex updated_date 2026/07/28

Abstract

We prove that a continuous potential q can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the perturbed biharmonic operator Δ_g²+q on a conformally transversally anisotropic Riemannian manifold of dimension ≥ 3 with boundary, assuming that the geodesic ray transform on the transversal manifold is constructively invertible. This is a constructive counterpart of the uniqueness result of [51]. In particular, our result is applicable and new in the case of smooth bounded domains in the 3-dimensional Euclidean space as well as in the case of 3-dimensional admissible manifolds.

Related

• Inverse boundary problems for biharmonic operators in transversally anisotropic geometries
• The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform
• Essential self-adjointness of perturbed biharmonic operators via conformally transformed metrics
• Uniqueness of a Potential from Boundary Data in Locally Conformally Transversally Anisotropic Geometries
• Biharmonic maps into a Riemannian manifold of non-positive curvature