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

Lili Yan

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arXiv · 2109.07712

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

Lili Yan

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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 $\Delta_g^2+q$ on a conformally transversally anisotropic Riemannian manifold of dimension $\ge 3$ 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.

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Lili Yan. 2021-09-16. Reconstructing a potential perturbation of the biharmonic operator on transversally anisotropic manifolds. https://arxiv.org/abs/2109.07712

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