  We prove that under certain assumptions a partial differential equation can
be derived from a variational principle. It is well-known from Noether's
theorem that symmetries of a variational functional lead to conservation laws
of the corresponding Euler-Lagrange equation. We reverse this statement and
prove that a differential equation which satisfies sufficiently many symmetries
and corresponding conservation laws leads to a variational functional whose
Euler-Lagrange equation is the given differential equation.
