On a variational principle of Hashin and Shtrikman

In this paper a simple derivation of a new version of the variational principle of Hashin and Shtrikman is given. It appears possible to dispense with some subsidiary conditions which in the original principle had to be imposed on the class of functions considered in the variational process. However, through the use of the new principle the possibility of obtaining a pair of two sided bounds is lost and this has to be compensated by invoking one of the complementary principles which are formulated in the sequel.