= Strong local minimizer of a variational integral
For a fixed-endpoint variational integral, an admissible function $u$ is a strong local minimizer if $I(v)\geq I(u)$ for all admissible $v$ whose <uniform norm> distance from $u$ is sufficiently small. Derivatives can be far apart. Hence strong local minimality implies <weak local minimizer of a variational integral>[weak local minimality], while a global minimizer implies both. Small narrow bumps and rapid low-amplitude oscillations explain why the reverse implication can fail.
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