Deriving the Euler-Lagrange Equations for the Chan-Vese Model

1. Is Lagrange equation same as Euler Lagrange equation?

Is Lagrange equation same as Euler Lagrange equation?

In this context Euler equations are usually called Lagrange equations. In classical mechanics, it is equivalent to Newton's laws of motion; indeed, the Euler-Lagrange equations will produce the same equations as Newton's Laws.