lemma A.484 Lower semicontinuity of the Douglas functional

open in the book · appendices/A-long-proofs.tex:23758 · p. 3030

Rests on

depends_on definition A.481 Douglas' boundary functional ¶
- depends_on definition A.476 Disc-type surfaces and the two functionals ¶
  - depends_on definition 13.22 First fundamental coefficients ¶
    - depends_on definition 13.21 First fundamental form ¶
      - depends_on definition 13.11 Arc length ¶
      - depends_on definition 13.18 Surface ¶
    - depends_on definition 13.19 Parameter curves ¶
      - depends_on definition 13.8 Curve ¶
      - depends_on definition 13.18 Surface ¶ ↺
  - depends_on equation 16.60 eq:calcvar-dirichlet-integral ¶
proves proof app:A-long-proofs@proof-286 ¶

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type	direction	node	provenance	where
`depends_on`	→	Douglas' boundary functional	declared	appendices/A-long-proofs.tex:23764
`proves`	←	app:A-long-proofs@proof-286	declared	appendices/A-long-proofs.tex:23767