Probabilistic approach to the Lam e equations of linear elastostatics

A probabilistic approach to systems of partial differential equations is developed on the basis of the well-known Feynman–Kac and Bismut formulas providing explicit probabilistic representations of the solutions and of their derivatives of scalar differential equations. Some numerical examples are also included. In particular the Lam e equations of elastostatics are solved and the results are compared with some known exact analytic solutions to demonstrate the efficiency of the approach.