Iterative reduction of the Dirichlet problem to the Neumann problem

An iteration procedure for reduction of the Dirichlet boundary-value problem to the Neumann problem is suggested. Estimates of the rate of convergence are established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 362–369, March, 1995.This paper was supported by the Foundation for Fundamental Research of the Ukrainian State Committee on Science and Technology and by the American Mathematical Society.