Recovery of non-smooth coefficients appearing in anisotropic wave equations

Abstract : We study the problem of unique recovery of a non-smooth one-form A and a scalar function q from the Dirichlet to Neumann map, Λ A,q , of a hyperbolic equation on a Riemannian manifold (M, g). We prove uniqueness of the one-form A up to the natural gauge, under weak regularity conditions on A, q and under the assumption that (M, g) is simple. Under an additional regularity assumption, we also derive uniqueness of the scalar function q. The proof is based on the geometric optic construction and inversion of the light ray transform extended as a Fourier Integral Operator to non-smooth parameters and functions.
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https://hal.archives-ouvertes.fr/hal-02073353
Contributor : Yavar Kian <>
Submitted on : Tuesday, March 19, 2019 - 6:48:16 PM
Last modification on : Saturday, March 30, 2019 - 2:06:33 AM

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Ali Feizmohammadi, Yavar Kian. Recovery of non-smooth coefficients appearing in anisotropic wave equations. 2019. ⟨hal-02073353⟩

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