Green's function [itex]G(x_0,y_0,x,y) =v(x_0,y_0,x,y) + h(x_0,y_0,x,y)[/itex] in a region [itex]\Omega \hbox { with boundary } \Gamma[/itex]. Also [itex]v(x_0,y_0,x,y) = -h(x_0,y_0,x,y)[/itex] on boundary [itex]\Gamma[/itex] and both [itex]v(x_0,y_0,x,y) \hbox { and }h(x_0,y_0,x,y)[/itex] are harmonic function in [itex]\Omega[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]v=\frac{1}{2}ln[(x-x_0)^2 + (y-y_0)^2] [/tex]

From the Max and Min proterty of Harmonic function in a region. The max and min value of the function is on the boundary of the region it is in.

In this case, G is defined as G=v+h and h=-v on the boundary.G=0 on the boundaryso both max and min equal to zero. Why is the book claimed G is negative or zero inside the region [itex]\Omega[/itex].

The book stated G is harmonic function in [itex] \Omega \;[/itex] and G=0 on [itex]\Gamma[/itex]. That pretty much lock in G=0 in [itex] \Omega \;[/itex].

See my post below what the book said word to word.

If G=0 in [itex] \Omega \;[/itex], then it is pretty useless!!! I am confused!!! Please help.

Thanks

Alan

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# Question on why the book claimed Green's function =< 0.

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