RECOVERY OF NONSMOOTH COEFFICIENTS APPEARING IN ANISOTROPIC WAVE EQUATIONS.

We study the problem of unique recovery of a nonsmooth one-form\scrA and a scalar function q from the Dirichlet to Neumann map,\Lambda\scrA,q, of a hyperbolic equation on a Riemannian manifold (M, g). We prove uniqueness of the one-form\scrA up to the natural gauge, under weak regularity conditions on\scrA, 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 nonsmooth parameters and functions. [ABSTRACT FROM AUTHOR]