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For the functional IL(v,λ)≡Iv(v)+∫ΩcλG(v)dxdy, what is the necessary condition for IL to have a stationary value?

For the functional IL(v,λ)≡Iv(v)+∫ΩcλG(v)dxdy, what is the necessary condition for IL to have a stationary value? Correct Answer δvxIL+δvyIL+δλIL=0

In the Lagrange multiplier method the constrained problem is reformulated as one of finding the stationary points of the unconstrained functional IL(v,λ)≡Iv(v)+∫ΩcλG(v)dxdy where λ(x,y) is the Lagrange multiplier. The necessary condition for IL to have stationary value is δvxIL+δvyIL+δλIL=0.

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