Subharmonic function: Difference between revisions

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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 make a [[convex cone]], that is, a linear combination of subharmonic functions with positive coefficients is also subharmonic.
with positive coefficients is also subharmonic.
 
*PointwiseThe pointwise maximum of two subharmonic functions is subharmonic.
 
*The limit of a decreasing sequence of subharmonic functions is subharmonic (or identicaly equal to