# Fundamental Lemma of Calculus of Variations

Fundamental Lemma Of Calculus Of Variations

In mathematics, specifically in the calculus of variations, the fundamental lemma of the calculus of variations states that if the definite integral of the product of a continuous function f(x) and h(x) is zero, for all continuous functions h(x) that vanish at the endpoints of the range of integration and have their first two derivatives continuous, then f(x)=0. This lemma is used in deriving the Euler–Lagrange equation of the calculus of variations. It is a lemma that is typically used to transform a problem from its weak formulation (variational form) into its strong formulation (differential equation).

Read more about Fundamental Lemma Of Calculus Of Variations:  Statement, Proof, The Du Bois-Reymond Lemma, Applications

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Fundamental Lemma Of Calculus Of Variations - Applications
... This lemma is used to prove that extrema of the functional are weak solutions (for an appropriate vector space ) of the Euler-Lagrange equation The Euler-Lagrange ...

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