theorem 16.60 Weierstrass' necessary condition

open in the book · parts/02-mathematical-methods/14-calculus-of-variations.tex:1754 · p. 650

Rests on

depends_on definition 16.13 Weak and strong extrema ¶
- depends_on definition 16.12 The two norms; weak and strong neighbourhoods ¶
  - depends_on definition 16.11 Admissible class; functional ¶
    - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on theorem 7.40 Continuous functions are integrable ¶
      - depends_on definition 7.39 Darboux sums and the definite integral ¶
      - depends_on theorem 7.24 Extreme value theorem ¶
      - depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      - proves proof ch:05-real-analysis@proof-23 ¶
  - depends_on definition 6.24 Metric ¶
    - depends_on definition 3.43 Map ¶
      - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.28 Set ¶
    - depends_on definition 3.38 Ordered pair and Cartesian product ¶
depends_on equation 16.51 eq:calcvar-excess ¶
proves proof ch:14-calculus-of-variations@proof-29 ¶

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type	direction	node	provenance	where
`depends_on`	→	Weak and strong extrema	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:1761
`depends_on`	→	eq:calcvar-excess	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:1761
`proves`	←	ch:14-calculus-of-variations@proof-29	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:1764