We point out in which cases an integral condition on the $\epsilon_{rs}$ (which has, for $n=3$, an interesting mechanical meaning) can be interpreted as a sufficient condition for the existence of solutions of the set of partial differential equations $1/2 (u_{r,s} + u_{r,s}) = \epsilon_{rs}$, $(r,s = 1, \cdots,n)$, where $\epsilon_{rs} \in L^{2}(A)$, $A$ being a bounded connected open set of $R^{n}$. Furthermore, we show how this condition allows an integral (weak) formulation of the elastic equilibrium problem, when the stress is taken as principal unknown instead of the displacement.