Theoretical analysis of magnetic cloaking problems using elliptical metamaterials

The conjugation problem and control problems for the 3D model of magnetostatics are considered. These problems are related to the design of three-dimensional magnetic cloaking shells. An elliptical metamaterial is chosen as a cloaking medium that fills a region which is topologically equivalent to a spherical layer. The solvability of boundary and control problems is proved, an optimality system is derived that describes the necessary conditions for an extremum, some properties of optimal solutions are established.