definition 10.79 Parabolic boundary

open in the book · parts/02-mathematical-methods/08-pdes.tex:2145 · p. 363

ground object -- no derivation owed

Rests on

depends_on definition 10.6 Type of a second-order operator ¶
- depends_on definition 10.4 The second-order operator ¶
  - depends_on definition 10.3 Principal part and principal symbol ¶
    - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - depends_on definition 10.1 Partial differential equation; order ¶
    - depends_on equation 10.2 eq:pde-multi-index ¶
  - depends_on proposition 7.105 Clairaut–Schwarz ¶
    - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on equation 7.7 eq:ana-limit-left ¶
      - depends_on equation 7.5 eq:ana-limit-right ¶
    - depends_on theorem 7.35 Mean value theorem ¶
      - depends_on proposition 7.29 Linearity ¶
      - depends_on theorem 7.34 Rolle ¶
      - proves proof ch:05-real-analysis@proof-19 ¶
    - proves proof ch:05-real-analysis@proof-64 ¶
- depends_on theorem 5.116 Sylvester's law of inertia ¶
  - depends_on definition 5.110 Bilinear map ¶
    - depends_on definition 5.37 Linear transformation ¶
      - depends_on definition 4.33 Vector space ¶
  - depends_on definition 5.111 Symmetric and antisymmetric forms ¶
    - depends_on definition 5.110 Bilinear map ¶ ↺
    - depends_on equation 5.137 eq:lin-bilinear-matrix ¶
  - depends_on equation 5.139 eq:lin-bilinear-congruence ¶
  - proves proof ch:03-linear-algebra-representations@proof-53 ¶
depends_on definition 6.3 Closed set ¶
- depends_on definition 3.35 Union, intersection, difference ¶
  - depends_on definition 3.8 Conjunction ¶
  - depends_on definition 3.9 Disjunction ¶
  - depends_on definition 3.7 Negation ¶
- depends_on definition 6.2 Open set ¶
  - depends_on definition 6.1 Topological space ¶
    - depends_on definition 3.31 Empty set ¶
    - depends_on definition 3.35 Union, intersection, difference ¶ ↺
    - depends_on definition 3.30 Subset ¶
    - depends_on equation 3.51 eq:set-indexed ¶

Supports

depends_on theorem 10.80 Parabolic maximum principle ¶
- depends_on corollary 10.81 Uniqueness for the heat equation ¶
- depends_on proposition A.163 The viscous problem produces the entropy inequality ¶

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`	→	Type of a second-order operator	declared	parts/02-mathematical-methods/08-pdes.tex:2155
`depends_on`	→	Closed set	declared	parts/02-mathematical-methods/08-pdes.tex:2155
`depends_on`	←	Parabolic maximum principle	declared	parts/02-mathematical-methods/08-pdes.tex:2169