proposition 10.91 Dirichlet principle

open in the book · parts/02-mathematical-methods/08-pdes.tex:2410 · p. 365

Rests on

depends_on definition 10.87 Weak form of an elliptic problem ¶
- depends_on definition 10.85 Sobolev space ¶
  - depends_on definition 12.2 Hilbert space ¶
    - depends_on definition 5.18 Inner product ¶
      - depends_on definition 4.33 Vector space ¶
    - depends_on definition 6.27 Convergence; Cauchy sequence; completeness ¶
      - depends_on definition 6.24 Metric ¶
    - depends_on equation 5.44 eq:lin-norm-assoc ¶
  - depends_on definition 10.83 Weak solution ¶
    - depends_on definition 17.38 Schwartz space and tempered distributions ¶
    - depends_on definition 10.3 Principal part and principal symbol ¶
      - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - depends_on equation 10.2 eq:pde-multi-index ¶
- depends_on definition 10.83 Weak solution ¶ ↺
depends_on theorem 10.88 Lax–Milgram ¶
- depends_on definition 12.2 Hilbert space ¶ ↺
- depends_on definition 10.87 Weak form of an elliptic problem ¶ ↺
- proves proof ch:08-pdes@proof-36 ¶
proves proof ch:08-pdes@proof-38 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Weak form of an elliptic problem	declared	parts/02-mathematical-methods/08-pdes.tex:2415
`depends_on`	→	Lax–Milgram	declared	parts/02-mathematical-methods/08-pdes.tex:2415
`proves`	←	ch:08-pdes@proof-38	declared	parts/02-mathematical-methods/08-pdes.tex:2418