Harnack’s principle

If the functionsu1(z), u2(z), …  are harmonic (http://planetmath.org/HarmonicFunction) in the domain  G  and


in every point of G, then  limnun(z)  either is infiniteMathworldPlanetmath in every point of the domain or it is finite in every point of the domain, in both cases uniformly (http://planetmath.org/UniformConvergence) in each closed (http://planetmath.org/ClosedSet) subdomain of G.  In the latter case, the function  u(z)=limnun(z)  is harmonic in the domain G (cf. limit function of sequence).

Title Harnack’s principle
Canonical name HarnacksPrinciple
Date of creation 2013-03-22 14:57:35
Last modified on 2013-03-22 14:57:35
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 14
Author Mathprof (13753)
Entry type Theorem
Classification msc 30F15
Classification msc 31A05