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arxiv: 1601.03347 · v1 · pith:RPDTRY4Lnew · submitted 2016-01-13 · 🧮 math.CV

A proof of Khavinson's conjecture in R⁴

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keywords mathbffunctionsharmonicproblemballboundedkhavinsonunit
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The paper deals with an extremal problem for bounded harmonic functions in the unit ball of $\mathbf{R}^4$. We solve the generalized Khavinson problem in $\mathbf{R}^4$. This precise problem was formulated by G. Kresin and V. Maz'ya for harmonic functions in the unit ball and in the half--space of $\mathbf{R}^n$. We find the optimal pointwise estimates for the norm of the gradient of bounded real--valued harmonic functions.

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