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In this paper, we consider a Cauchy problem for the Poisson equation with nonhomogeneous source. The problem is shown to be ill-posed as the solution exhibits unstable dependence on the given data function. Using a new method, we regularize the given problem and obtain some new results. Two numerical examples are given to illustrate the effectiveness of our method.

On a general filter regularization method for the 2D and 3D Poisson equation in physical geodesy