Bounds for the Electrical Resistance for Non-homogeneous Two-dimensional Conducting Body

A mathematical model is developed to determine the steady-state current flow through in non-homogeneous isotropic conductor whose shape is a two-dimensional hollow domain. The corresponding electric boundary value problem is formulated using Maxwell's theory of electricity. The determination of the two-dimensional motion of charges is based on the concept of the electrical conductance. The Cauchy-Schwarz inequality is used to get the lower and upper bounds for the electrical conductance. The derived upper and lower bound formulae are illustrated by numerical examples.