Mathematics – Analysis of PDEs
Scientific paper
2011-08-09
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.
Hartenstine David
Rudd Matthew
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