Subharmonic Function

Let be an open set and a real-valued continuous function on . Suppose that for each closed disk and every real-valued harmonic function defined on a neighborhood of which satisfies on , it holds that on the open disk . Then is said to be subharmonic on (Krantz 1999, p. 99).

1. If are subharmonic on , then so is .

2. If is subharmonic on and is a constant, than is subharmonic on .

3. If are subharmonic on , then $max{f_1(z),f_2(z)}$ is also subharmonic on .

See also

Barrier, Harmonic Function

Explore with Wolfram|Alpha

More things to try:

References

Krantz, S. G. "The Dirichlet Problem and Subharmonic Functions." §7.7 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 97-101, 1999.

Referenced on Wolfram|Alpha

Subharmonic Function

Cite this as:

Weisstein, Eric W. "Subharmonic Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SubharmonicFunction.html

Subject classifications