I am not making much progress on this one folks. Any help would be much appreciated...
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The lines $ \ y=x \ $ and $ \ x=1 \ $ divide the plane into four wedges. Let $S$ be the one which is above $ \ y=x \ $ and to the left of $ \ x=1 $. Find a function $\phi(x,y)$ which is harmonic in $S$ and satisfies $ \ \phi=2 \ $ on the vertical part of the boundary of $S$ and $ \ \phi=-8 \ $ on the slanted part of the boundary of $S$.
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If I am not mistaken, we cannot use the form $ \ A \ Arg(z) \ + \ B \ $ due to the fact that the non-positive axis lies inside the region of interest. But I am not sure where to go from there. I am also a little confused about what adjustment (if any) is needed since the lines do not intersect at the origin (as opposed to all the wedge examples I have seen before this).