科研之友
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摘要
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 < infinity. An example demonstrates that, in general, these formulas do not hold in a non-asymptotic sense.
- 出版日期2011
