theorem A.491 Dirichlet problem for the disc; quoted

open in the book · appendices/A-long-proofs.tex:24091 · p. 3033

Rests on

depends_on definition 16.67 The Dirichlet principle ¶
- depends_on equation 16.32 eq:calcvar-euler-lagrange-field ¶
- depends_on equation 16.34 eq:calcvar-laplace ¶
depends_on definition 10.66 Harmonic function ¶
- depends_on definition 7.98 Functions of class $C^{1}$ ¶
  - depends_on definition 7.20 Continuity at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on equation 7.7 eq:ana-limit-left ¶
    - depends_on equation 7.5 eq:ana-limit-right ¶
  - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶ ↺
      - depends_on definition 7.9 Real function ¶ ↺
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶
- depends_on equation 10.24 eq:pde-poisson-equation ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`cites` (context)	→	Methods of Mathematical Physics, Volume II: Partial Differential Equations	derived	appendices/A-long-proofs.tex:24109
`depends_on`	→	The Dirichlet principle	declared	appendices/A-long-proofs.tex:24110
`depends_on`	→	Harmonic function	declared	appendices/A-long-proofs.tex:24110