A BOHR PHENOMENON FOR ELLIPTIC EQUATIONS - AIZENBERG, LEV; TARKHANOV, NIKOLAI (Proceedings of the London Mathematical Society, 2001)
In 1914 Bohr proved that there is an $r \in (0,1)$ such that if a power series converges in the unit disk and its sum has modulus less than $1$ then, for $|z| < r$, the sum of absolute values of its terms is again less than $1$. Recently, analogous results have been obtained for functions of several variables. The aim of this paper is to place the theorem of Bohr in the context of solutions to second-order elliptic equations satisfying the maximum principle. 2000 Mathematics Subject Classification: 35J15, 32A05, 46A35.