Vol. 226, No. 1, 2006

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Algebraic structure of quasiradial solutions to the γ-harmonic equation

Vladimir G. Tkachev

Vol. 226 (2006), No. 1, 179–200
Abstract

We obtain an explicit representation for quasiradial γ-harmonic functions, which shows that these functions have an essentially algebraic nature. We give a complete description of all γ that admit algebraic quasiradial solutions. Unlike the cases γ = and γ = 1, only finitely many algebraic solutions are shown to exist for any fixed |γ| > 1. A special extremal series of γ corresponds exactly to the well known ideal m-atomic gas adiabatic constant γ = (2m + 3)(2m + 1).

Keywords
γ-harmonic function, quasiradial solution, algebraic function
Mathematical Subject Classification 2000
Primary: 35J15
Secondary: 31A05, 14H05
Milestones
Received: 16 October 2004
Revised: 28 January 2005
Accepted: 15 February 2005
Published: 1 July 2006
Authors
Vladimir G. Tkachev
Mathematical Department
Volgograd State University
2-ja Prodolnaja 30 Volgograd
400062 Russia
http://www.math.kth.se/~tkatchev