# Superharmonic function

From Encyclopedia of Mathematics

A function $u(x)$ of a point $x$ of a Euclidean space $\mathbf R^n$, $n\geq1$, or of a harmonic space such that $-u(x)$ is a subharmonic function.

#### Comments

A function that is both subharmonic and superharmonic is said to be a harmonic function.

**How to Cite This Entry:**

Superharmonic function.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Superharmonic_function&oldid=31742

This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article