theorem 16.56 Sufficiency of the second variation
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:1664
· p. 649
Rests on
- depends_on equation 16.49 eq:calcvar-jacobi ¶
- depends_on equation 16.45 eq:calcvar-second-variation ¶
- proves proof ch:14-calculus-of-variations@proof-28 ¶
Supports
- depends_on corollary 16.65 Sufficiency for a weak minimum ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | eq:calcvar-jacobi | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1670 |
depends_on |
→ | eq:calcvar-second-variation | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1670 |
depends_on |
← | Sufficiency for a weak minimum | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1971 |
proves |
← | ch:14-calculus-of-variations@proof-28 | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1673 |