Calculus of Variations and Geometric Measure Theory

B. Kawohl - J. Manfredi - M. Parviainen

Solutions of nonlinear PDEs in the sense of averages

created by kawohl on 16 Jan 2011


Submitted Paper

Inserted: 16 jan 2011

Year: 2011


We characterize $p$-harmonic functions including $p=1$ and $p=\infty$ by using mean value properties extending classical results of Privaloff from the linear case $p=2$ to all $p$'s. We describe a class of random tug-of-war games whose value functions approach $p$-harmonic functions as the step goes to zero for the full range $1<p<\infty$.