  We derive an explicit formula for global weak solutions of the one
dimensional system of pressure-less Euler-Poisson equations. Our variational
formulation is an extension of the well-known formula for entropy solutions of
the scalar inviscid Burgers' equation: since the characteristics of the
Euler-Poisson equations are parabolas, the representation of their weak
solution takes the form of a "quadratic" version of the celebrated Lax-Oleinik
variational formula. Three cases are considered. (i) The variational formula
recovers the "sticky particle" solution in the attractive case; (ii) It
represents a repulsive solution which is different than the one obtained by the
sticky particle construction; and (iii) the result is further extended to the
multi-dimensional Euler-Poisson system with radial symmetry.
