Mean value properties of harmonic functions and related topics (a survey)

2019/04/15 by Kuznetsov, Nikolay
#31A05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1904.08312

Abstract

Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes of functions.

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• Inverse mean value properties (a survey)
• Mean value property for nonharmonic functions
• The mean value property (corrected version)
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• Asymptotic mean value properties of meta- and panharmonic functions