Properties
- A function is harmonic if and only if it is both subharmonic and superharmonic.
- If is C2 (twice continuously differentiable) on an open set in, then is subharmonic if and only if one has
- on
- where is the Laplacian.
- The maximum of a subharmonic function cannot be achieved in the interior of its domain unless the function is constant, this is the so-called maximum principle. However, the minimum of a subharmonic function can be achieved in the interior of its domain.
- Subharmonic functions are upper semicontinuous, while superharmonic functions are lower semicontinuous.
Read more about this topic: Subharmonic Function
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