A proof of the generalized Khavinson conjecture

TL;DR

This paper provides a complete proof of the generalized Khavinson conjecture, establishing that for bounded harmonic functions on the unit ball in ^n, the optimal constants for radial derivatives and gradients are equal.

Contribution

It offers the first complete proof confirming the conjecture that the sharp constants for radial derivatives and gradients of bounded harmonic functions are identical.

Findings

Confirmed the equality of sharp constants for radial derivatives and gradients

Established the conjecture for all dimensions n

Advanced understanding of harmonic function estimates

Abstract

We give a complete proof of the generalized Khavinson conjecture which states that, for bounded harmonic functions on the unit ball of $\mathbb{R}^n$, the sharp constants in the estimates for their radial derivatives and for their gradients coincide.