SOLUTION OF THE DIRICHLET PROBLEM FOR THE INHOMOGENEOUS LAME SYSTEM WITH LOWER ORDER COEFFICIENTS

摘要

We consider the Dirichlet problem for the inhomogeneous Lamé system in the plane with constant leading coefficients in a (finite or infinite) domain, bounded by a Lyapunov contour. For domains of finite diameter we use the weighted Hölder class of functions with power behavior at infinity. We propose an equivalent reduction of the problem to a system of Fredholm integral equations in the domain and on the boundary contour.