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arXiv · 1108.1982

Asymptotic statistical characterizations of p-harmonic functions of two variables

David Hartenstine·Matthew Rudd
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Abstract

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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David Hartenstine, Matthew Rudd. 2011-08-09. Asymptotic statistical characterizations of p-harmonic functions of two variables. https://doi.org/10.1216/rmj-2011-41-2-493

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