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Dirichlet's principle

In mathematics, and particularly in potential theory, Dirichlet's principle is the assumption that the minimizer of a certain energy functional is a solution to Poisson's equation.

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Formal statement

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Dirichlet's principle

Nodes22
Edges21
Triples36
Avg. degree1.91
Density0.090909
Components1

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Dirichlet's principle

Top relations

related to References · 22
Dirichlet's principle → American Mathematical Society, Calculus, Conformal Mapping, Courant, Dirichlet's, Eric, Evans, Hildebrandt, HolkemaWeisstein, InterscienceLawrence, ISBN, Mariano, MathWorld, Minimal Surfaces, Monna, Oosthoek, Partial Differential Equations, Scheltema, Schiffer, SpringerA
related to history · 8
Dirichlet's principle → Bernhard Riemann, Carl Friedrich Gauss, Dirichlet's, Karl Weierstrass, Peter Gustav Lejeune Dirichlet, Riemann, The, Weierstrass's
related to Formal statement · 3
Dirichlet's principle → Dirichlet's, Omega, Poisson's
is a · 1
Dirichlet's principle → assumption that the minimizer of a certain energy functional is a solution to Poisson's equation

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Important terminology

dirichlet's principle functional dirichlet function displaystyle integral riemann example calculus variations assumption minimizer energy solution poisson's equation boundary mathematics differentiable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dirichlet's principleis aassumption that the minimizer of a certain energy functional is a solution to Poisson's equation0.90text
Carl Friedrich Gaussinstance ofand others0.80text
Peter Gustav Lejeune Dirichletinstance ofand others0.80text
Dirichlet's principlerelated to Formal statementDirichlet's0.60section
Dirichlet's principlerelated to Formal statementPoisson's0.60section
Dirichlet's principlerelated to Formal statementOmega0.60section
Dirichlet's principlerelated to historyThe0.60section
Dirichlet's principlerelated to historyDirichlet's0.60section
Dirichlet's principlerelated to historyBernhard Riemann0.60section
Dirichlet's principlerelated to historyRiemann0.60section
Dirichlet's principlerelated to historyCarl Friedrich Gauss0.60section
Dirichlet's principlerelated to historyPeter Gustav Lejeune Dirichlet0.60section

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