Let 
be harmonic functions on a connected open set
.
Then either 
uniformly on compact sets or there is a finite-values harmonic
function 
on 
such that 
uniformly on compact sets.
See also
Harmonic Function, Harnack's Inequality
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References
Krantz, S. G. "Harnack's Principle." §7.6.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 97, 1999.
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Cite this as:
Weisstein, Eric W. "Harnack's Principle." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HarnacksPrinciple.html