# $|Du|^2$ is subharmonic if $u$ is harmonic.

In Evan's textbook "Partial Differential Equation", question 5 in section 2.5 says "$|Du|^2$ is subharmonic if $u$ is harmonic.". This can be easily proven, but do we really need the derivative $D$? I don't see any point of taking the derivative of $u$.

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Is this property used latter in the book? –  Davide Giraudo Oct 4 '12 at 20:18