theorem 16.90 Noether's first theorem, several independent variables

open in the book · parts/02-mathematical-methods/14-calculus-of-variations.tex:2848 · p. 663

Rests on

depends_on equation 16.32 eq:calcvar-euler-lagrange-field ¶
depends_on equation 16.33 eq:calcvar-field-first-variation ¶
depends_on theorem 16.84 Noether's first theorem, one independent variable ¶
- depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
- depends_on equation 16.75 eq:calcvar-invariance ¶
- depends_on proposition 16.17 The first variation of an integral functional ¶
  - depends_on equation 16.11 eq:calcvar-basic-functional ¶
  - depends_on equation 16.14 eq:calcvar-gateaux ¶
  - proves proof ch:14-calculus-of-variations@proof-7 ¶
- proves proof ch:14-calculus-of-variations@proof-39 ¶
proves proof ch:14-calculus-of-variations@proof-42 ¶

Supports

depends_on theorem 16.93 Noether's second theorem ¶
- depends_on example 16.109 The Einstein–Hilbert action ¶
- depends_on theorem 44.19 Covariant conservation of stress–energy ¶
  - depends_on proposition 44.20 Perfect-fluid equations of motion ¶
    - depends_on corollary 44.21 Dust flows on geodesics ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
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inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:calcvar-euler-lagrange-field	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:2869
`depends_on`	→	eq:calcvar-field-first-variation	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:2869
`depends_on`	→	Noether's first theorem, one independent variable	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:2869
`depends_on`	←	Noether's second theorem	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:2979
`proves`	←	ch:14-calculus-of-variations@proof-42	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:2873