ISOPERIMETRIC-INEQUALITIES FOR AN ELECTROSTATIC PROBLEM

We study the problem of the (p-)capacity c(p) of a multiconnected configuration OMEGA = (G\E)\(or(i) H(i)), when partial derivative G and partial derivative E have given potentials. Here OMEGA represents a non homogeneous medium and the H(i), which separate the different connected components of OMEGA, represent perfect conductors. We give isoperimetric inequalities.for c(p) and the unknown potentials on H(i), by comparison with a similar configuration with spherical symmetry.