APM  Vol.5 No.11 , September 2015
Mean-Value Theorems for Harmonic Functions on the Cube in Rn
Abstract: Let be a hypercube in Rn. We prove theorems concerning mean-values of harmonic and polyharmonic functions on In(r), which can be considered as natural analogues of the famous Gauss surface and volume mean-value formulas for harmonic functions on the ball in and their extensions for polyharmonic functions. We also discuss an application of these formulas—the problem of best canonical one-sided L1-approximation by harmonic functions on In(r).
Cite this paper: Petrov, P. (2015) Mean-Value Theorems for Harmonic Functions on the Cube in Rn. Advances in Pure Mathematics, 5, 683-688. doi: 10.4236/apm.2015.511062.

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