Let be an open disk, and let be a harmonic function on such that for all . Then for all , we have
Harnack's Inequality
See also
Harmonic Function, Harnack's Principle, Liouville's Conformality TheoremExplore with Wolfram|Alpha
References
Flanigan, F. J. "Harnack's Inequality." §2.5.1 in Complex Variables: Harmonic and Analytic Functions. New York: Dover, pp. 88-90, 1983.Krantz, S. G. "The Harnack Inequality." §7.6.1 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 97, 1999.Referenced on Wolfram|Alpha
Harnack's InequalityCite this as:
Weisstein, Eric W. "Harnack's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HarnacksInequality.html