A closed-form solution of the Lame equation of elasticity

Classical Lame equations of the theory of elasticity are considered from the point of view of the probabilistic Feynman-Kac formula, which delivers exact solutions of many elliptic and parabolic boundary value problems. Unlike other approaches which are applicable only for certain domains of special shape, the Feynman-Kac solutions are applicable to domains of practically arbitrary shape, and their implementations does not involve any special functions.