Minimum Principle for the Tikhonov Functional in the Problem of Stable Continuation of a Potential Field from a Surface

We consider the ill-posed problem of continuation of a potential field into a cylindrical domain from a surface in three-dimensional space. An approximate solution of the problem is constructed that is stable with respect to the given field. The continuation of the potential field is carried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical domain of rectangular cross-section. Tikhonov’s regularization method is used to construct a stable solution of the problem.