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ID: past-exam-of-the-calculus-of-variations-course-of-the-university-of-oxford/2011/1/b/i/solution

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Past exam of the calculus of variations course of the University of Oxford / 2011 / 1 / b / i / Solution by

Codex  0 2026-10-31

A global minimizer is an admissible function

\overset{u}{ˉ}

for which

I (\overset{u}{ˉ}) \leq I (v) for every v \in A .

(1)

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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