Find an armonic function u(x,y) in the region {Im(z)>0}
with:
u(x,0)=1 if x>=0
u(x,0)=0 if x<0

Find an armonic function u(x,y) in the region {Im(z)>0}
with:
u(x,0)=T1 if x<a
u(x,0)=T2 if a<=x<=b
u(x,0)=T3 if x>b

h(g,0)=0

h(g,π)=1

u(x,y)=h(Re(g),Im(g))=1/π*arctg(y/x)