A Bohr Phenomenon For Elliptic Equations |
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| Authors: | Aizenberg Lev; Tarkhanov Nikolai |
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| Institution: | Department of Mathematics and Computer Science, Bar-Ilan University 52900 Ramat-Gan, Israel; e-mail: aizenbrg{at}macs.biu.ac.il
Universität Potsdam, Institut für Mathematik Postfach 60 15 53, 14415 Potsdam, Germany; e-mail: tarkhan{at}math.uni-potsdam.de |
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| Abstract: | In 1914 Bohr proved that there is an r  (0,1) such that if apower series converges in the unit disk and its sum has modulusless than 1 then, for |z| < r, the sum of absolute valuesof its terms is again less than 1. Recently, analogous resultshave been obtained for functions of several variables. The aimof this paper is to place the theorem of Bohr in the contextof solutions to second-order elliptic equations satisfying themaximum principle. 2000 Mathematics Subject Classification: 35J15, 32A05, 46A35. |
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| Keywords: | elliptic equation Harnack inequality series expansion harmonic function |
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