Upper and lower bounds are given for the Dirichlet integral, principally based upon an extension of a method of G. Polya and G. Szego. Numerical bounds are calculated for the capacitance of the five regular solids. In particular, it is found that the number 1.3351 is an upper bound for the capacitance of a cube of side 2.0, an improvement over all upper bounds previously known.
展开▼
