The Location of Singularities of Two-Dimensional Harmonic Functions. II: Applications
ROBERT F. MILLAR · SIAM Journal on Mathematical Analysis · 1970
The procedure developed in Part I is applied to two examples, the intention in each case being to illustrate some feature of the method. For the first example, a previously considered problem is reexamined ; here the boundary C in the w-plane is \[ w = \exp - i\kappa (x + ib\cos \kappa x),\quad 0 \leqq x \leqq {{2\pi } / \kappa },\] and the two singularities are located precisely. For the second example, C is taken to be an ellipse ; the singularities at the foci are found.