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 (), J. Serrin (), and J. Moser (, ) generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Perelman's solution of the Poincaré conjecture uses a version of the Harnack inequality, found by R. Hamilton (), for the Ricci flow. Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic functions. Harnack's inequality can also be used to show the interior regularity of weak solutions of partial differential equations.
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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 (), J. Serrin (), and J. Moser (, ) generalized Harnack's inequality to solutions of elliptic or parabolic partial differential equations. Perelman's solution of the Poincaré conjecture uses a version of the Harnack inequality, found by R. Hamilton (), for the Ricci flow. Harnack's inequality is used to prove Harnack's theorem about the convergence of sequences of harmonic functions. Harnack's inequality can also be used to show the interior regularity of weak solutions of partial differential equations.
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En mathématiques, l'inégalité ...... tions aux dérivées partielles.
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In de wiskunde is de ongelijkh ...... het inwendige van haar domein
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In der Mathematik geben Harnac ...... dem Mathematiker Axel Harnack.
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In mathematics, Harnack's ineq ...... artial differential equations.
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Nierówność Harnacka – twierdze ...... jemnych funkcji harmonicznych.
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Неравенство Гарнака — если фун ...... следующие неравенства: , где .
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数学におけるハルナックの不等式(ハルナックのふとうしき、英: ...... 方程式の弱解の内部での正則性を示すためにも使うことができる。
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738,607,946
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Carl Gustav Axel Harnack
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Harnack theorem
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En mathématiques, l'inégalité ...... tions aux dérivées partielles.
@fr
In de wiskunde is de ongelijkh ...... de regelmatigheid van de func
@nl
In der Mathematik geben Harnac ...... dem Mathematiker Axel Harnack.
@de
In mathematics, Harnack's ineq ...... artial differential equations.
@en
Nierówność Harnacka – twierdze ...... jemnych funkcji harmonicznych.
@pl
Неравенство Гарнака — если фун ...... следующие неравенства: , где .
@ru
数学におけるハルナックの不等式(ハルナックのふとうしき、英: ...... 方程式の弱解の内部での正則性を示すためにも使うことができる。
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Harnack's inequality
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Harnack-Ungleichung
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Inégalité de Harnack
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Nierówność Harnacka
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Ongelijkheid van Harnack
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Неравенство Гарнака
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ハルナックの不等式
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