Question: The Laplace operator is defined by = xx + yy . A function u(x, y) satisfying the Laplace equation u =

The Laplace operator Δ is defined by Δƒ = ƒxx + ƒyy. A function u(x, y) satisfying the Laplace equation Δu = 0 is called harmonic.

Show that if u(x, y) is harmonic, then the partial derivatives ∂u/∂x and ∂u/∂y are harmonic.

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