# Reconstruction in the Calder\'on problem on conformally transversally anisotropic manifolds

@article{Feizmohammadi2020ReconstructionIT, title={Reconstruction in the Calder\'on problem on conformally transversally anisotropic manifolds}, author={Ali Feizmohammadi and Katya Krupchyk and Lauri Oksanen and Gunther Uhlmann}, journal={arXiv: Analysis of PDEs}, year={2020} }

We show that a continuous potential $q$ can be constructively determined from the knowledge of the Dirichlet-to-Neumann map for the Schrodinger operator $-\Delta_g+q$ on a conformally transversally anisotropic manifold of dimension $\geq 3$, provided that the geodesic ray transform on the transversal manifold is constructively invertible. This is a constructive counterpart of the uniqueness result of Dos Santos Ferreira-Kurylev-Lassas-Salo. A crucial role in our reconstruction procedure is…

## 4 Citations

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

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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 ∆ g + q on a conformally transversally…

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In this article we investigate inverse problems of heat and wave equations involving fractional Laplacian operator with zeroth order nonlinear perturbations. The study of inverse problems involving…

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