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