I am a freshman in micromechanics area. Many books and papers always say the linear elastic equilibrium equation(Someone also called Navier type function) could be solved with Green Function and Fourier Transformation, but without details. May be the writers think anyone should know these two popular methods in solving the PDE. I have search many books(both mathmatic and mechanics), However, there are little information about solving the navier type function with those two methods. 

If you know any book about this area, please do not hesitate to tell me. Because the question has frustrated me for a long time. Your kind reply will be greate appreciated!!!