Harnack's inequality

Harnack's inequality

In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by
*Citation | last1=Hamilton | first1=Richard S. | title=The Harnack estimate for the Ricci flow | id=MathSciNet | id = 1198607 | year=1993 | journal=Journal of Differential Geometry | issn=0022-040X | volume=37 | issue=1 | pages=225–243
*citation|first=A. |last=Harnack|title=Die Grundlagen der Theorie des logarithmischen Potentiales und der eindeutigen Potentialfunktion in der Ebene|publisher=V. G. Teubner|place= Leipzig |year=1887|url=http://www.archive.org/details/vorlesunganwend00weierich
*springer|id=h/h046620|title=Harnack theorem|first=L.I.|last= Kamynin
*springer|id=H/h046600|first1=L.I.|last1= Kamynin|first2=L.P.|last2= Kuptsov
*Citation | last1=Moser | first1=Jürgen | title=On Harnack's theorem for elliptic differential equations | id=MathSciNet | id = 0159138 | year=1961 | journal=Communications on Pure and Applied Mathematics | issn=0010-3640 | volume=14 | pages=577–591
*Citation | last1=Moser | first1=Jürgen | title=A Harnack inequality for parabolic differential equations | id=MathSciNet | id = 0159139 | year=1964 | journal=Communications on Pure and Applied Mathematics | issn=0010-3640 | volume=17 | pages=101–134
*Citation | last1=Serrin | first1=James | title=On the Harnack inequality for linear elliptic equations | id=MathSciNet | id = 0081415 | year=1955 | journal=Journal d'Analyse Mathématique | issn=0021-7670 | volume=4 | pages=292–308
*L. C. Evans (1998), "Partial differential equations". American Mathematical Society, USA. For elliptic PDEs see Theorem 5, p. 334 and for parabolic PDEs see Theorem 10, p. 370.


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