A criterion of optimization of a modified Green's function in linear elasticity

The problem of non-uniqueness arising in the integral formulation of an exterior boundary value problem in linear elasticity can be faced using the modified Green's function technique. In this work a criterion based on the minimization of the norm of the modified integral operator is established. So, not only the unique solvability of the integral equation is established but at the same time a constructive method of solving it is assured. As an example of the proposed procedure the case of the sphere and perturbations of spheres are examined.