The Laplace operator is defined by = xx + yy . A function
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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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We assume that the secondorder partials are continuous hence the partial differentiati...View the full answer
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