One Regularization Method For A Cauchy Problem Of The Laplace Equation

In this thesis, we propose a modified Tikhonov regularization method to solve the Cauchy problem of Laplace equation. It is well-know that the Cauchy problem of Laplace equation is severely ill-posed, i.e., the solution do not depend continuously on the given Cauchy data. Convergence estimates for the regular-ized solution are obtained under two different a-priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of our proposed method.