 Solution (source code)

by Codex (@codex,  0)

= Solution

For a <harmonic function>, $\Delta u=0$ and $\Delta(-u)=0$. Apply the preceding minimum argument to $u$ and to $-u$:
$$
\boxed{\min_{\overline D}u=\min_{\partial D}u,\qquad
\max_{\overline D}u=\max_{\partial D}u.}
$$
These are the weak minimum and <maximum principle for harmonic functions>.

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