Infima of Families of Superharmonic Functions

Abstract

If Г is a class of extended real-valued functions on a set D, a function υ on D will be called a majorant [minorant] of Г if $\upsilon u\left[ {\upsilon u} \right]$ for every u in Г. If D is an open subset of ℝ _N , the least superharmonic majorant [greatest subharmonic minorant] of Г, if such a function exists, will be denoted by LM _D Г [GM _D Г], or by LM _D u [GM _D u] if Г = {u} is a singleton.