Determination of a general solution of three-dimensional Lamé equations of elasticity theory

We integrate the Lamé equation and find new solutions in the case of three-dimensional elasticity theory, which are expressed in terms of harmonic functions. We prove that the solution obtained involves only three independent functions. In a curvilinear orthogonal coordinate system, a general solution of the Lamé equation is expressed in terms of three harmonic functions. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 1, pp. 109–116, January–March, 2006.