Harmonic Function: Analyticity, Compactness and Minimum Value
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Let (attached) be a function that is analytic and not constant throughtout a bounded domain (attached) and continuous (attached) on its boundary (here domain is an open connected set).
Prove, by considering (attached) , that the component function (attached) has a minimum value in the compact region (attached) which occurs on (attached) and never in (attached).
Use this result to formulate and prove a minimum principle for harmonic functions.
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