Thin inclusions of large or small conductivity in an anisotropic homogeneous medium

The work is devoted to the calculation of electro or thermostatic fields in an anisotropic homogeneous medium containing a thin inclusion with other conductive properties. Thin inclusions which conductive coefficients are much larger or much smaller than the coefficients of the host medium have the prime interest for applications. For both cases, the problem is reduced to the solution of integral equations on the middle surface of thin inclusions. Explicit solutions of these equations in the case of thin ellipsoidal inclusions and a constant external field are obtained for a homogeneous medium with arbitrary anisotropy. The dependence of the solution on the orientation of the inclusion and the characteristics of the anisotropy are analyzed. For non-interacting inclusions, the effective conductive properties of an anisotropic media containing a random set of thin inclusions are presented.