Definition:Superharmonic Function

Definition

Let $D$ be a complex domain.

A superharmonic function is a continuous real-valued function $f$ such that for every closed disk $\map {B^-} {a; r} \subseteq D$ with center $a$ and radius $r$:

$\ds \map f a \ge \int_0^{2 \pi} \map f {a + r e^{i \theta} } \rd \theta$

Also see

• Definition:Subharmonic Function
• Definition:Circumferential Mean

• Results about superharmonic functions can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): subharmonic function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): subharmonic function