  This paper studies the regularity properties of the density of the exit
measure for super-Brownian motion with (1+\beta)-stable branching mechanism. It
establishes the continuity of the density in dimension d=2 and the
unboundedness of the density in all other dimensions where the density exists.
An alternative description of the exit measure and its density is also given
via a stochastic integral representation. Results are applied to the
probabilistic representation of nonnegative solutions of the partial
differential equation \Delta u=u^{1+\beta}.
