Math Help - PDE seperation of var question

1. PDE seperation of var question

Use separation of variables to solve

$\bigtriangledown^2 u = 0$, in D, u = f, on $\partial u$

if D is the semi-circle of radius 1 centred at the origin and above the x-axis where f = 1 on the circular boundary, f = 0 on the flat part

2. At first sight the 'contour conditions' seem to be a little 'conflictual': waht's the value of f(*,*) in [1,0] and [-1,0]?... 0 or 1?...

Kind regards

$\chi$ $\sigma$
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