In variational approach of Finite Element Method, if the functional has more than one dependent variable, extremizing it would give us as many number of differential equations as the number of dependent variables. A many number of differential equations would mean that we get as many number of weak form statements.

When there is a single dependent variable in the functional, we can get the functional back from the weak form statement / principle of virtual work. But when there are large number of weak form statements, how can we get the functional back from these weak form statements?