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In this paper, we address a Cauchy problem for elliptic equations with inhomoge- neous 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 di erent regularized methods. Moreover, convergence estimates are established under some priori assumptions on the exact solution. Some numerical examples are given to illuminate the e ect of our methods. Keywords and phrases: Cauchy problem; Ill-posed problem; Convergence estimates. Mathematics subject Classification 2000: 35K05, 35K99, 47J06, 47H10

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