A potential function method for the Cauchy problem of elliptic operators

In this paper, we deal with the Cauchy problem of elliptic operators. Through the use of a single-layer potential function, we devise a numerical method for approximating the solution of the Cauchy problem of elliptic operators, which are well known to be highly ill-posed in nature. The method is based on the denseness of single-layer potential functions. Convergence and stability estimates are then given with some examples for numerical verification on the efficiency of the proposed method. It has been observed that the use of more Cauchy data will greatly improve the accuracy of the approximate solutions.