Operators of minimal norm via modified Green's function for the elastic two-dimensional case using the simple multipole coefficients

The problem of non-uniqueness arising in the integral formulation of an exterior boundary value problem for the elastic two-dimensional case can be faced using the fundamental solution technique. In this work a criterion based on the minimization of the norm of the modified integral operator is established using simple multipole coefficients. As an example of the proposed procedure the case of the circle and perturbations of circle are examined.