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Harnack's inequality

In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by A. Harnack (1887). Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic functions. J. Serrin (1955), and J. Moser (1961, 1964) generalized Harnack's inequality to…

Overview, Elliptic partial differential equations & Proof of Harnack's inequality in a ball

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Overview

Harmonic functionA.Harnack1993Harnack's theoremJ.Serrin
13 related topics

Elliptic partial differential equations

Elliptic partial differential equationsSupremumNorm
3 related topics

Proof of Harnack's inequality in a ball

Poisson's formulaUnit sphere
2 related topics

Parabolic partial differential equations

Heat equationPositive definite
2 related topics

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Overview

Proof of Harnack's inequality in a ball

Elliptic partial differential equations

Parabolic partial differential equations

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Harnack's inequality

Nodes25
Edges24
Triples14
Avg. degree1.92
Density0.08
Components1

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Harnack's inequality

Top relations

related to The statement · 5
Harnack's inequality → Harnack's, In, It, R2, Rn
related to Parabolic partial differential equations · 4
Harnack's inequality → Harnack's, Let, PDEs, There
related to Elliptic partial differential equations · 3
Harnack's inequality → For, Harnack's, The
is a · 1
Harnack's inequality → inequality relating the values of a positive harmonic function at two points

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Important terminology

inequality harnack's differential equations elliptic partial harmonic parabolic theorem harnack isbn displaystyle function constant positive solution used solutions ball see

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Harnack's inequalityis ainequality relating the values of a positive harmonic function at two points0.90text
heat equation.Let Minstance ofParabolic partial differential equationsThere is a version of Harnack's inequality for linear parabolic PDEs0.80text
Harnack's inequalityrelated to Elliptic partial differential equationsFor0.60section
Harnack's inequalityrelated to Elliptic partial differential equationsHarnack's0.60section
Harnack's inequalityrelated to Elliptic partial differential equationsThe0.60section
Harnack's inequalityrelated to Parabolic partial differential equationsThere0.60section
Harnack's inequalityrelated to Parabolic partial differential equationsHarnack's0.60section
Harnack's inequalityrelated to Parabolic partial differential equationsPDEs0.60section
Harnack's inequalityrelated to Parabolic partial differential equationsLet0.60section
Harnack's inequalityrelated to The statementHarnack's0.60section
Harnack's inequalityrelated to The statementRn0.60section
Harnack's inequalityrelated to The statementIt0.60section

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