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math.AP2012
On the existence and uniqueness of p-harmonious functions
Hannes Luiro, Mikko Parviainen, Eero Saksman
We give a self-contained and short proof for the existence, uniqueness and measurability of so called -harmonious functions. The proofs only use elementary analytic tools. As a…
math.AP2012
Local approximation of superharmonic and superparabolic functions in nonlinear potential theory
Juha Kinnunen, Teemu Lukkari, Mikko Parviainen
We prove that arbitrary superharmonic functions and superparabolic functions related to the -Laplace and the -parabolic equations are locally obtained as limits of supersolut…