Abstract
Let G be an open subset of ℝn, n ⩾ 1. The classical theorem on the averages over balls for the Laplace equation states that a necessary and sufficient condition for harmonicity of function \( f \in C\left( G \right) \) is that
for all \( x \in G,0 < r < dist\left( {x,\partial G} \right) \).
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© 2003 Springer Science+Business Media Dordrecht
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Volchkov, V.V. (2003). Mean Value Characterization of Various Classes of Functions. In: Integral Geometry and Convolution Equations. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0023-9_31
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DOI: https://doi.org/10.1007/978-94-010-0023-9_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3999-4
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