DEBT
发表于 2025-3-25 06:53:57
General Variational FormulasIn the first two chapters we have investigated the rate of change of variational integrals ℱ with respect to variations of the dependent variables. In particular, we have derived the necessary conditions . and .for extremizers u of ℱ, and suitable modifications of these conditions were shown to hold for constrained extremizers.
fluffy
发表于 2025-3-25 09:32:54
Second Variation, Excess Function, ConvexityIf .(u) is a real valued function of a real variable which is of class .. on ℝ, then, besides .′(u.) = 0, also the condition .″(u.) ≥ 0 is necessary for .. being a local minimizer of .. Moreover, the conditions . are sufficient for .. furnishing a local minimum.
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