  We consider self-similar potential flow for compressible gas with polytropic
pressure law. Self-similar solutions arise as large-time asymptotes of general
solutions, and as exact solutions of many important special cases like Mach
reflection, multidimensional Riemann problems, or flow around corners.
Self-similar potential flow is a quasilinear second-order PDE of mixed type
which is hyperbolic at infinity (if the velocity is globally bounded). The type
in each point is determined by the local pseudo-Mach number L, with L<1 resp.
L>1 corresponding to elliptic resp. hyperbolic regions. We prove an ellipticity
principle: the interior of a parabolic-elliptic region of a sufficiently smooth
solution must be elliptic; in fact $L$ must be bounded above away from 1 by a
domain-dependent function. In particular there are no open parabolic regions.
We also discuss the case of slip boundary conditions at straight solid walls.
