Two Regularized Solutions of an Ill-Posed Problem for the Elliptic Equation With Inhomogeneous Source

Nguyen Huy Tuan, Tran Thanh Binh

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 different regularized methods. Moreover, convergence estimates are established under some priori assumptions on the exact solution. Some numerical examples are given to illuminate the effect of our methods.