Asymptotic statistical characterizations of $p$-harmonic functions of two variables
Asymptotic statistical characterizations of $p$-harmonic functions of two variables
Generalizing the well-known mean-value property of harmonic functions, we prove that a p-harmonic function of two variables satisfies, in a viscosity sense, two asymptotic formulas involving its local statistics. Moreover, we show that these asymptotic formulas characterize p-harmonic functions when 1 < p < \infty. An example demonstrates that, in …