In this note we show that if the areal mean-value theorem holds for a plane domain (subject to a mild regularity condition) for all integrable harmonic functions, then the domain must be a disk. It is ...

Hypergeometric functions occupy a central role in mathematical analysis by encapsulating a diverse class of series that extend many classical functions. Equally, identities involving harmonic numbers ...

We derive a mean value property for p-harmonic functions in two dimensions, 1 < p < ∞, which holds asymptotically in the viscosity sense. The formula coincides with the classical mean value property ...