The problem of conjugation of solutions of the Lamé equation in domains with piecewise smooth boundaries (Q2387078)

The paper computes the conjugating solutions of the Lamé equations in areas with piecewise smooth boundaries and investigates the asymptotic behavior of the solutions. An application of these results is that the solutions of the Lamé equation can be represented by using generalized elastic potentials of the plain fiber and of the double layer problem. A significant theorem proves when the conjugation problem is solvable. It is as follows: Under the hypothesis when the singular points of the piecewise-smooth surface satisfy the characteristic equations together with some additional integral bounds, then the conjugation problem is solvable.