On discrete neumann problem in a quadrant

Abstract

We study a discrete analogue on the Neumann boundary value problem for elliptic pseudo-differential equation in a quadrant. This approach is based on a special factorization of an elliptic symbol which permits to construct a general solution for a discrete pseudo-differential equation in discrete analogues of Sobolev-Slobodetskii spaces. The discrete Neumann boundary conditions are considered in the paper. Unique solvability of discrete Neumann boundary value problem is proved and a comparison between discrete and continuous solutions is given