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Partial Differential Equations : Harmonic Function and Constant Function

Suppose U is a positive harmonic function which is defined everywhere in the plane. Show that U must be a constant function.

This is a question regarding Poisson Integral Formula in PDE. I need to find it using the Harnak's inequalities.

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A harmonic function is shown to be a constant function. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.