A degenerate elliptic problem from subsonic-sonic flows in convergent nozzles

<p style="text-indent:20px;">This paper concerns continuous subsonic-sonic potential flows in a two dimensional convergent nozzle, which is governed by free boundary problem of quasilinear degenerate elliptic equation. It shown that for given nozzle perturbation an straight one, and mass flux, there exists uniquely flow whose velocity vector along the normal direction at inlet sonic curve. Furthermore, curve this boundary, where singular sense speed only <inline-formula><tex-math id="M1">\begin{document}$ C^{1/2} $\end{document}</tex-math></inline-formula> Hölder acceleration blows up state.</p>