Mikko Parviainen

most citedEquivalence of Viscosity and Weak Solutions for the

p (x)

-Laplacian

30 citations · 36 across the 3 of their papers we have counts for

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math.AP2012★ 6 cited

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…

math.AP2010

Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces

Jasun Gong, Juan J. Manfredi, Mikko Parviainen

We show that quasi-minimizers of non-homogeneous energy functionals on metric measure spaces are locally Hölder continuous and satisfy the Harnack inequality. We assume that the sp…

math.AP2010★ 30 cited

Equivalence of Viscosity and Weak Solutions for the $p (x)$ -Laplacian

Petri Juutinen, Teemu Lukkari, Mikko Parviainen

We consider different notions of solutions to the $p (x)$ -Laplace equation $-÷(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with $1 < p (x) < \infty$ . We show by proving a comparison principle that vi…

Harnack's inequality for p-harmonic functions via stochastic games

Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces

Equivalence of Viscosity and Weak Solutions for the p(x)-Laplacian

Equivalence of Viscosity and Weak Solutions for the $p (x)$ -Laplacian