Question: We must prove that if u(x,y) is a harmonic function on the domain D=B_r(z_0) and that u(x,y) extends continuously on the boundary of D. Then

We must prove that if u(x,y) is a harmonic function on the domain D=B_r(z_0) and that u(x,y) extends continuously on the boundary of D. Then u(x,y) can only obtain its maximum value on the boundary D unless u(x,y) is a constant function.

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