The identical approximation regularization method for the inverse problem to a 3D elliptic equation with variable coefficients

In this article, the Cauchy problem for a 3D elliptic equation is considered in a cylindrical domain. To regularize the problem, we propose a regularization method named 'identical approximation regularization', which does not require complicated calculations. Two identical approximate regularization solutions are compared in the numerical section. The experimental results show that the Dirichlet reconstruction solution is more effective than the others.