Fundamental lemma of the calculus of variations

Initial result in using test functions to find extremum

In mathematics, specifically in the calculus of variations, a variation δf of a function f can be concentrated on an arbitrarily small interval, but not a single point. Accordingly, the necessary condition of extremum appears in a weak formulation integrated with an arbitrary function δf. The fundamental lemma of the calculus of variations is typically used to transform this weak formulation into the strong formulation, free of the integration with arbitrary function. The proof usually exploits the possibility to choose δf concentrated on an interval on which f keeps sign. Several versions of the lemma are in use. Basic versions are easy to formulate and prove. More powerful versions are used when needed.

This keyword could refer to multiple things. Here are some suggestions: