An integral equation of elasticity

In this work a certain mixed problem in R for the Lamé equations in the theory of elasticity is reduced to the integral equation An explicit formula for the solutions is given for either Ω = {x:x₂ > 0} or Ω = {x:∥x∥<r}. The question of smoothness of the solutions is also discused. Another formulae on Ω = {x:∥x∥<r} are found in 5], 4]. It seems that the techniques used below allows a deeper investigation of properties of the solutions to problem (*).