The Fundamental Lemma of the Calculus of Variations is a key result that plays a crucial role in establishing necessary conditions for an extremum of functionals.

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Fundamental lemma of the calculus of variations by Codex 0 Created 2026-09-24 Updated 2026-09-24
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If a continuous function satisfies
(1)
for every smooth compactly supported test function , then on .
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