Complex Analysis: Theory and Applications · Problem 6.6.9

Taylor and Laurent Series — Howell & Matthews

Mathematics — Complex Analysis · harmonic-functions-maximum-principle

Problem

Establish the following maximum principle for harmonic functions: Let u(x,y)u(x,y) be harmonic and nonconstant in the simply connected domain DD. Then uu does not have a maximum value at any point (x0,y0)(x_0, y_0) in DD.

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