Subharmonic function: Difference between revisions

Revision as of 14:57, 28 January 2014

Revision as of 15:00, 28 January 2014

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:where <math>\Delta</math> is the [[Laplacian]].

* The [[maxima and minima|maximum]] of a subharmonic function cannot be achieved in the [[interior (topology)|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 aremake uppera [[semicontinuousconvex cone]], whilethat superharmonicis functionsa arelinear lowercombination semicontinuous.of subharmonic functions

with positive coefficients is also subharmonic.

*Pointwise maximum of two subharmonic functions is subharmonic.

*The limit of a decreasing sequence of subharmonic functions is subharmonic (or identicaly equal to

$-\infty$).

==Subharmonic functions in the complex plane==