Mathematics · Partial Differential Equations

Let B be the unit ball in &mathbb;R; 3 centered at the origin. The Euler-Lagrange equation corresponding to the functional I(u) = 1 2 ∫ B |∇u| 2 dx - 1 5 ∫ B |u| 5 dx is:

Verified Solution4 OptionsUpdated: October 2026👁️1 View

Correct answer

Δu = -|u| 3 u

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Let B be the unit ball in &mathbb;R; 3 centered at the origin. The Euler-Lagrange equation corresponding to the functional I(u) = 1 2 &int; B |&nabla;u| 2 dx - 1 5 &int; B |u| 5 dx is: