Abstract
In this paper, we study a Cauchy problem of an elliptic equation in a multi-dimensional case. Such a problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. To overcome the ill-posedness of the model problem, a new regularization method is applied to solve it. The corresponding error estimates between the exact solution and its regularization approximation are given. Finally, two numerical experiments are provided to illustrate the main results.
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