Algebraic structure of quasiradial solutions to the $γ$-harmonic equation

Details Algebraic structure of quasiradial solutions to the $γ$-harmonic equation Algebraic structure of quasiradial solutions to the $γ$-harmonic equation

2007-09-27

arxiv.org/abs/0709.4472v1

Pacific J. Math., 226 (2006), no. 1, 179-200

Physics

Mathematical Physics

21 pages

Scientific paper

We obtain an explicit representation for quasiradial $\gamma$-harmonic functions, which shows that these functions have essentially algebraic nature. In particular, we give a complete description of all $\gamma$ which admit algebraic quasiradial solutions. Unlike the cases $\gamma=\infty$ and $\gamma=1$, only finitely many algebraic solutions is shown to exist for any fixed $|\gamma|>1$. Moreover, there is a special extremal series of $\gamma $ which exactly corresponds to the well-known ideal $m$-atomic gas adiabatic constant $\gamma=\frac{2m+3}{2m+1}$.

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