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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To N. N. Uraltseva with deep respect
Translated from Problemy Matematicheskogo Analiza99, 2019, pp. 3-21.
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Kuznetsov, N. Mean Value Properties of Harmonic Functions and Related Topics (a Survey). J Math Sci 242, 177–199 (2019). https://doi.org/10.1007/s10958-019-04473-w
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DOI: https://doi.org/10.1007/s10958-019-04473-w