Fundamental Lemma of CoV and the Euler-Lagrange Equations

Sat, 30 May 2026 00:00:00 +0000

This is the first entry in a series on the Euler-Lagrange Equations and the Calculus of Variations. The first main result I prove is the Fundamental Lemma of the Calculus of Variations. It’s a small but important result, used not only in CoV but also in the modern theory of Partial Differential Equations, where it underpins the definition of distributional derivatives. For that reason, I want to discuss it first.

Calculus of Variations on Victor's Blog

Fundamental Lemma of CoV and the Euler-Lagrange Equations