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.
Harnack's Principle
See also
Harmonic Function, Harnack's InequalityExplore with Wolfram|Alpha
References
Krantz, S. G. "Harnack's Principle." §7.6.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 97, 1999.Referenced on Wolfram|Alpha
Harnack's PrincipleCite this as:
Weisstein, Eric W. "Harnack's Principle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HarnacksPrinciple.html