# Euler-Lagrange equation

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## Euler-Lagrange equation

[¦ȯi·lər lə′grānj i‚kwā·zhən]
(mathematics)
A partial differential equation arising in the calculus of variations, which provides a necessary condition that y (x) minimize the integral over some finite interval of f (x,y,y ′) dx, where y ′ = dy/dx; the equation is (δƒ(x,y,y ′)/δ y) - (d/dx)(δƒ(x,y,y ′)/δ y ′) =0. Also known as Euler's equation.
References in periodicals archive ?
Then the solution of the problem (2) satisfies the following Euler-Lagrange equation
A possible way to accelerate the process is to deal with Euler-Lagrange equation through a TV filter [24].
We provide a growth condition on L to guarantee that u is locally bounded and, by building suitable variations, we prove the validity of the Euler-Lagrange equation without imposing differentiability on L.
This equation can be derived as the Euler-Lagrange equation for the minimization problem:
We consider the Euler-Lagrange equation using the identity of Proposition 4.
Topics increase in mathematical complexity as the book progresses to encompass dozens of examples including a derivation of the Euler-Lagrange equation, heat flow and analytic functions, and a bicycle wheel and the Gauss-Bonnet theorem.
The Euler-Lagrange equation tells us that on the turnpike the marginal product of capital must match the rate of change in the valuation of investment.

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