The quasi-reversibility regularization method for a Cauchy problem for the Laplace equation

Juanjuan Pu, Xiangtuan Xiong

Ill-posed problem; the Cauchy problem for the Laplace equation; Quasi-reversibility regularization; Error estimate.

In this paper, the Cauchy problem for the homogeneous and nonhomogeneous Laplace equation in a strip domain is discussed. Where the Cauchy data atis given, and the solution is found in the interval (0,1). The corresponding error estimation is obtained by a new quasi-reversibility regularization method with a appropriate regularization parameter selection.

https://dx.doi.org/10.31873/IJEAS.7.11.01