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Hào, D.N., Van, T.D. and Gorenflo, R. (1992) Towards the Cauchy Problem for the Laplace Equation. Partial Differential Equations, 111.

has been cited by the following article:

• TITLE: Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation

  AUTHORS: Hongwu Zhang, Xiaoju Zhang

  KEYWORDS: Ill-Posed Problem, Cauchy Problem, Semi-Linear Elliptic Equation, Filtering Function Method, Convergence Estimate

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.12, December 17, 2015

  ABSTRACT: A Cauchy problem for the semi-linear elliptic equation is investigated. We use a filtering function method to define a regularization solution for this ill-posed problem. The existence, uniqueness and stability of the regularization solution are proven; a convergence estimate of Hölder type for the regularization method is obtained under the a-priori bound assumption for the exact solution. An iterative scheme is proposed to calculate the regularization solution; some numerical results show that this method works well.