Local approximation of superharmonic and superparabolic functions in   nonlinear potential theory
  We prove that arbitrary superharmonic functions and superparabolic functions related to the $p$-Laplace and the $p$-parabolic equations are locally obtained as limits of supersolutions with desired convergence properties of the corresponding Riesz measures. As an application we show that a family of uniformly bounded supersolutions to the $p$-parabolic equation contains a subsequence that converges to a supersolution. 
Juha Kinnunen, Teemu Lukkari, Mikko Parviainen
math.AP