Asymptotic statistical characterizations of p-harmonic functions of two variables

Details Asymptotic statistical characterizations of p-harmonic functions of two variables Asymptotic statistical characterizations of p-harmonic functions of two variables

2011-08-09

arxiv.org/abs/1108.1982v1

Rocky Mountain Journal of Mathematics, Volume 41, Number 2, 2011 pp.493-504

Mathematics

Analysis of PDEs

Minor changes from published version: updated author info., one updated reference

Scientific paper

10.1216/RMJ-2011-41-2-493

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 general, these formulas do not hold in a non-asymptotic sense.

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