Mathematics · Higher Mathematics
Let B be the unit ball in &DoubleStruckCapitalR;3 centered at the origin. The Euler-Lagrange equation corresponding to the functional I(u) = ∫B (1 + |∇u|2)1/2 dx is:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1(1 + |∇u|2)Δu = ∑i,j=13 uxiuxjuxi,xj
- 2|∇u| = 1
- 3Δu(1 + |∇u|2)1/2 = 1
- 4div∇u(1 + |∇u|2)1/2 = 0✓
Correct answer
div∇u(1 + |∇u|2)1/2 = 0
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