Harnack's principle
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In complex analysis, Harnack's principle or Harnack's theorem is one of several closely related theorems about the convergence of sequences of harmonic functions, that follow from Harnack's inequality.
If the functions u1(z), u2(z), ... are harmonic in an open subset G of the complex plane C, and
in every point of G, then the limit
either is infinite in every point of the domain G or it is finite in every point of the domain, in both cases uniformly in each closed subset of G. In the latter case, the function
is harmonic in the set G.
[edit] References
- Kamynin, L.I. (2001), “Harnack theorem”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
- This article incorporates material from Harnack's principle on PlanetMath, which is licensed under the GFDL.
