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We derive three results on the inverse problem of determining the Lamé parameters λ(x) and μ(x) for an isotropic elastic body from its Dirichlet-to-Neumann map.

In this article we consider the Schrδdinger operator in R n ,n ^ 3, with electric and magnetic potentials which decay exponentially as \x\ -> oo. We show that the scattering amplitude at fixed positive energy determines the electric potential and the magnetic field.

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We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation. As a by-product we prove a similar result for the nonself-adjoint hyperbolic operator with time-independent coefficients.−V (x, t)u = 0,