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 cylindricaldomain from a surface in three-dimensional space. An approximate solution of the problem isconstructed that is stable with respect to the given field. The continuation of the potential field iscarried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical domainof rectangular cross-section. Tikhonov's regularization method is used to construct a stablesolution of the problem.