Problem with displacements for the three-dimensional Bianchi equation

Abstract

We consider the Bianchi equation in a rectangular 3D parallelepiped G. For this equation, we analyze the problem of finding a regular solution on the basis of three given linear relations each of which relates the values of the unknown function at 60 points lying on the faces of G and inside the domain. We obtain sufficient conditions for the unique solvability of the problem in terms of the coefficients of these relations. © 2010 Pleiades Publishing, Ltd.