Formal Definition
Formally, the definition can be stated as follows. Let be a subset of the Euclidean space and let
be an upper semi-continuous function. Then, is called subharmonic if for any closed ball of center and radius contained in and every real-valued continuous function on that is harmonic in and satisfies for all on the boundary of we have for all
Note that by the above, the function which is identically −∞ is subharmonic, but some authors exclude this function by definition.
Read more about this topic: Subharmonic Function
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