31 citations · 103 across the 32 of their papers we have counts for
4 papers · 1 filter
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…
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…
Harnack's inequality for p-harmonic functions via stochastic games
Hannes Luiro, Mikko Parviainen, Eero Saksman
We give a proof of Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of…
Discontinuous gradient constraints and the infinity Laplacian
Petri Juutinen, Mikko Parviainen, Julio D. Rossi
Motivated by tug-of-war games and asymptotic analysis of certain variational problems, we consider a gradient constraint problem involving the infinity Laplace operator. We prove t…