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I tried to minimize below integral by finding field $\phi (x)$

$E = \int (D \ddot{\phi}^2(x) + C \dot{\phi}^2(x)) dx$

which $C$ and $D$ are constants. Could anyone help me? any answers are highly appreciated. I could guess an answer by dimensional analysis, but it is not enough and I need a detailed answer.

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    do you know about euler-lagrange equations? – 2017-02-17
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    As I now it includes a first derivative, not second derivative. Could you solve the problem? @Basti – 2017-02-17

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