A BOHR PHENOMENON FOR ELLIPTIC EQUATIONS

A BOHR PHENOMENON FOR ELLIPTIC EQUATIONS

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 seve...

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Veröffentlicht in:Proceedings of the London Mathematical Society 2001-03, Vol.82 (2), p.385-401
Hauptverfasser: AIZENBERG, LEV, TARKHANOV, NIKOLAI
Format: Artikel
Sprache:eng
Schlagworte:
elliptic equation
harmonic function
Harnack inequality
series expansion
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Zusammenfassung: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.
ISSN:0024-6115
1460-244X
DOI:10.1112/S0024611501012813