a regularization method for a cauchy problem of laplace's equation in an annular domain

in this paper, we propose a new regularization method based on a finite-dimensional subspace generated from fundamental solutions for solving a cauchy problem of laplace's equation in an annular domain. based on a conditional stability for the cauchy problem of laplace's equation, we obtain a convergence estimate under the suitable choice of a regularization parameter and an a-priori bound assumption on the solution. a numerical example is provided to show the effectiveness of the proposed method from both accuracy and stability.