Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneous flexural rigidity coefficient in the Euler-Bernoulli steady-state beam theory in the presence of a prescribed load is presented. Mathematically, this study is an extension to higher-order differential equations of the coefficient identification problem analysed by Marcellini (1982) for the one-dimensional Poisson equation. In addition, various types of boundary conditions are discussed. Conditions for the well-posedness of these inverse problems are established and, furthermore, numerical results obtained using a regularization algorithm are presented.