Harnack's Principle

Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u on U such that u_j->u uniformly on compact sets.

See also

Harmonic Function, Harnack's Inequality

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Krantz, S. G. "Harnack's Principle." §7.6.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 97, 1999.

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Harnack's Principle

Cite this as:

Weisstein, Eric W. "Harnack's Principle." From MathWorld--A Wolfram Web Resource.

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