Explaining Laplacian Vanishing for Harmonic Functions: A Physical Analysis

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avocadogirl
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Why does the laplacian vanish for harmonic functions? Can someone explain this in physical terms?
 

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I guess..answers for the Laplace eqn. are harmonic functions..so to find such solution one will equate to zero. (Laplace eqn. is already equated to zero).
This is my guess..
 

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