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Harmonic Functions

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Please help me with the following Problem:

Let u and v harmonic functions in R^n. Show that Î" (uv) = 2u .v where is the gradient.

Show also that if u is an harmonic function, then Î" (u^2) ¥ 0. For which (harmonic) functions is Î" (u^2) = 0 ?

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Harmonic functions are demonstrated in this solution.

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