A new filtering method for the Cauchy problem of the Laplace equation

Abstract

In the present paper, we consider a Cauchy problem for the Laplace equation in a rectangle domain. A new filtering method is presented for approximating the solution of this problem, and the Hölder-type error estimates are obtained by the different parameter choice rules. Numerical illustration shows that the proposed method works effectively.

Keywords:

• Cauchy problem for the Laplace equation
• error estimate
• filtering regularization
• ill-posed problem
• parameter choice rule

2010 AMS Subject Classification:

• 47A52

Acknowledgements

We would like to thank immensely the reviewers for their very constructive comments and suggestions which have helped us improving the paper. The project is supported by the Natural Science Foundation of Jiangsu Province of China for Young Scholar (No. BK20130118), the Fundamental Research Funds for the Central Universities (No. JUSRP1033), the China Postdoctoral Science Foundation (No. 2012M521742) and the NNSF of China (No. 11171136).