ABSTRACT
Suppose il is an open simply-connected polygon which has a sim ple boundary a = <r0 U a l9 where a0, (J\ are some of its connected parts, and set a0 H cr\ consists of two points, u is a bounded solution of the boundary-value problem
v is a (single-valued) harmonic function conjugate to u. Then, evidently, the function
Figure 26
where C is an arbitrary constant, conformally maps the polygon ft lying in the complex plane z, z = x + ¿y, onto the strip |Re ( | < 7r /4 . Under the mapping, the sraight line Re £ = ( —l ) fc7r /4 , k — 0,1, is the image of the set cr\crk. The common endpoints of the polygonal lines cr0, ai g° 1° infinity. We can (uniquely) choose the constant C such that the point defined on o \ cr0 is mapped into the point £ = 7r /4 .
