On nonconvex optimization with integral constraints

We consider the problem of minimizing f(y)dm with y dm=c,c fixed. The functionf is assumed to be continuous, but need not be convex. For this problem, we give necessary and sufficient conditions for the existence of solutions. We also give conditions under which uniqueness in a certain sense holds, and we show a relation which holds between the minimizers of two different problems and the corresponding values of the constraintsc.This research was supported by FINEP-Brazil, Grant Nos. 62.24-0416-00 and 4.2.82.0719-00.