  We study the domain of existence of a solution to a Riemann problem for the
pressure gradient equation in two space dimensions. The Riemann problem is the
expansion of a quadrant of gas of constant state into the other three vacuum
quadrants. The global existence of a smooth solution was established in Dai and
Zhang [Arch. Rational Mech. Anal., {\bf 155}(2000), 277-298] up to the free
boundary of vacuum. We prove that the vacuum boundary where the system is
degenerate is the trivial coordinate axes.
