Characteristic monopoles and variational estimates for the capacitance of tube capacitors. (Q1432311)

The problem of determining the capacitance and the electrostatic field of a cylindrical capacitor is reduced to the Dirichlet problem for the Laplace equation in a doubly connected bounded plane domain. This problem is equivalent to the constructing of a conformal mapping of a doubly connected domain onto an annulus. A variational solution scheme based on the generalized Gauss variational principle and on the concepts of characteristic multipoles and polarizabilities of higher orders is constructed. A sequence of new general inequalities for the capacitance of the cylindrical capacitor is built.