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A BOHR PHENOMENON FOR ELLIPTIC EQUATIONS

Published online by Cambridge University Press:  05 March 2001

LEV AIZENBERG  and
NIKOLAI TARKHANOV
LEV AIZENBERG
Affiliation:
Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israelaizenbrg@macs.biu.ac.il
NIKOLAI TARKHANOV
Affiliation:
Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam, Germanytarkhan@math.uni-potsdam.de
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Abstract

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.

Keywords

elliptic equationHarnack inequalityseries expansionharmonic function
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 82 , Issue 2 , March 2001 , pp. 385 - 401
Copyright
2001 London Mathematical Society

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