Carolyn Harnach lives in Chicago, Illinois. Companies in which she has a work history include Lcsw and Licensed Certified Social Worker. Positions she has held include Social Worker.
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What is Harnach's Instagram?
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What is Harnach's famous for?
In mathematics, Harnack's inequality is an inequality relating the values of a positive harmonic function at two points, introduced by A. Harnack (1887). J. Serrin (1955), 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 (1993), 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.. You can find more here.
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