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Answer by Zarrax for Solving Laplace's equation on semi-annular domain

The solution form you have written is for a disk not an annulus or half-annulus Separation of variables can be used in your half-annulus too, and the form you will get is$$A + B\ln r +...

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Solving Laplace's equation on semi-annular domain

Solve the following boundary value problems for the Laplace equation on the semi-annular domain:$ 1 < x^2 + y^2 < 2, y > 0 $$u(x, y) = 0, x^2 + y^2 = 1, u(x, y) = 1, x^2 + y^2 = 2, u(x, 0) =...

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