For circular region, why is ?
Where is the outward unit normal of .
Let circular region with radius . Let be harmonic function in .
The Green's function for Polar coordinate is found to be:
Where is the angle of and is the angle of the two points used in Steiner Invertion.
Next I want to solve the Dirichlet problem using Green's function. For any value of a hamonic function . The standard formular for Dirichlet problem is:
But the book just simply use Which is only a simple derivative of G respect to where in this case !!!
I don't understant how:
How can a normal derivative become and simple derivative respect to only? I know but the magnitude is not unity like the unit normal. Can anyone explain to me?