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Probelm in calculating a First Variation

  1. May 1, 2012 #1
    Hello,

    I am reading a paper on evolution problems of the type

    u(0) = 0
    u' (t) = v (t)
    v(t) = argmin {G (t, u(t), v(t)}

    The authour claims that the Euler Lagrange equation related to the last equation is

    dG / dv = 0 (1)

    I can not understand this.

    The Euler Equation formally can be written as

    dG / du - d (dG/dv) / dx (2)

    and this equation will be satisifed by u.

    But as the authour says, v satisfies
    dG / dv = 0 (3)

    u is the primitive of u, hence it should satisfy
    d (dG/dv) / dx (4)

    and this is different from (2)!

    Any help please? I am confused. I attach the paper for completeness, equation (10) in the paper's introduction is the problem, which is self-contained between equations (4) and (10), quick to read for somebody with a clue...

    Thank you!
     

    Attached Files:

  2. jcsd
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