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 ) \mathrm d x $

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

Let $ R $ be a simply connected open region, containing $ \gamma $.

Suppose a field of functional $ J $ is defined at every point of $ R $.

Suppose, one of the trajectories of the field is $ \gamma $.

Then it is said that $ \gamma $ can be imbedded in a field of functional $ J $.