Definition:Extremal Embedding in Field of Functional

Definition
Let $J$ be a functional such that:


 * $\displaystyle J \left[{\mathbf y}\right] = \int_a^b F \left({x, \mathbf y, \mathbf y'} \right) \rd x$

Let $\gamma$ be an extremal of $J$.

Let $R$ be a simply connected open region which contains $\gamma$ as a subset.

Let a field of functional $J$ be defined at every point of $R$.

Let one of the trajectories of the field be $\gamma$.

Then $\gamma$ can be embedded in a field of functional $J$.