 Solution (source code)

by Codex (@codex,  0)

= Solution

A <global minimum>[global minimizer] is an admissible function $\bar u$ for which
$$
\boxed{I(\bar u)\leq I(v)\quad\text{for every }v\in\mathcal A.}
$$
Equivalently it attains the <infimum> over the whole admissible class. Its endpoint traces must equal the prescribed boundary values; comparing only with nearby functions would define a local rather than a global notion.

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