Data recovering problem using moments theory and applications to some inverse problems

In this paper, the Cauchy problem for Laplace equation is investigated. By Green’s formulation,the problem can be transformed to two moment problems: the first one permits to complete the Dirichlet condition and the second to complete the Neumann condition on the boundary. We propose a numerical algorithm for solving the moment problem using Legendre polynomials and discuss the error estimation in the reconstruction of the solution. Then, we present applications to some inverse problems: Robin coefficient determination and cracks identification. Some numerical results are given to show the efficiency of the proposed method.