A proof of Khavinson's conjecture in R4. Issue 4 (21st April 2017) - Kalaj, David
Abstract: The paper deals with an extremal problem for bounded harmonic functions in the unit ball of R 4 . We solve the generalized Khavinson problem in R 4 . This precise problem was formulated by Kresin and Maz'ya for harmonic functions in the unit ball and in the half‐space of R n . We find the optimal pointwise estimates for the norm of the gradient of bounded real‐valued harmonic functions.