A new wavelet method for solving an ill-posed problem

摘要

So far there are many papers which deal with the Cauchy problem for elliptic equation. However, most of them are devoted to the case of constant coefficients. In this paper, we consider a Cauchy problem for an elliptic equation with variable coefficients. Due to ill-posedness of this problem, we provide a regularization method – wavelet dual least squares method to solve the problem. Via Meyer wavelet bases with a special project method dual least squares method, we can obtain error estimate between the regularized solution and exact solution.