Two regularized solutions of an ill-posed problem for the elliptic equation with inhomogeneous source

Abstract

In this paper, we address a Cauchy problem for elliptic equations with inhomogeneous
source data. The problem is shown to be ill-posed as the solution exhibits an unstable dependence
on the given data functions. Here, we shall deal with this problem by using two
dierent regularized methods. Moreover, convergence estimates are established under some
priori assumptions on the exact solution. Some numerical examples are given to illuminate
the eect of our methods.