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

Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion