Identification of a constant coefficient in an elliptic equation

The identification of an unknown constant coefficient in the main term of elliptic second order differential equation kMu + g(x)u = f(x) with the Dirichlet boundary condition is considered. The elliptic operator M is self-adjoint and bounded in  [image omitted]. The identification of k here is based on an integral boundary data. The local existence and uniqueness theorem for the inverse problem is proved in the class of the pairs involving a function  [image omitted] and a positive real number k. The uniqueness is obtained by a new approach.