A Bohr phenomenon for elliptic equations (Q2766395)

This article is devoted to the generalization of the well-known theorem of Bohr about the existence of a number \(r\in(0,1)\) such that if a power series \(\sum^\infty_{\nu=0}c_\nu z^\nu\) converges in the unit disk and the modulus of its sum is less than 1, then \(\sum^\infty_{\nu=0}|c_\nu z^\nu|<1\) for \(|z|<r\) to the case of functions of many variables. Thus the authors consider the classes of harmonic, separately harmonic and pluriharmonic functions. They prove the existence of explicit formulas for the greatest such number \(r\). Moreover they show that it is not possible to establish the corresponding result for solutions of elliptic equations of order larger than 2 and even for some second-order elliptic equations.