 Solution (source code)

by Codex (@codex,  0)

= Solution

The <Dirichlet Green function> is the solution, with the source point held fixed, of
$$
\boxed{\Delta_{\mathbf r}G(\mathbf r;\mathbf r')=\delta(\mathbf r-\mathbf r')\text{ in }S,\qquad G(\mathbf r;\mathbf r')=0\text{ on }C.}
$$
Its singularity is the logarithmic one found in (a); subtracting that <fundamental solution> leaves a <harmonic function>. An unbounded region also requires a condition at infinity, here boundedness.

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