Necessary condition for minimum: ∂²L/∂(ẏ)² ≥ 0 along extremal path. Strong + weak Legendre conditions. Conjugate-point analysis (Jacobi) extends. Distinguishes minima from saddles in variational problems.
Necessary condition for minimum: ∂²L/∂(ẏ)² ≥ 0 along extremal path. Strong + weak Legendre conditions. Conjugate-point analysis (Jacobi) extends. Distinguishes minima from saddles in variational problems.