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Difference between revisions of "Superharmonic function"

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A function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091230/s0912301.png" /> of a point <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091230/s0912302.png" /> of a Euclidean space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091230/s0912303.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091230/s0912304.png" />, or of a harmonic space such that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/s/s091/s091230/s0912305.png" /> is a [[Subharmonic function|subharmonic function]].
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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|subharmonic function]].
  
  

Latest revision as of 15:44, 15 April 2014

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://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
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