Fundamental lemma of the calculus of variations

If a continuous function

f

satisfies

\int_{a}^{b} f (x) η (x) d x = 0

for every smooth compactly supported test function

η

, then

f = 0

on

(a, b)

.

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Fundamental lemma of the calculus of variations by

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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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