Absolutely continuous states of exit measures for super-Brownian motions with branching restricted to a hyperplane

The exit measures of super-Brownian motions with branching mechanism from a bounded smooth domain D in ℝ^d+1 are known to be absolutely continuous with respect to the surface area on ϑD if whereas in the case they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely continuous states for alld≥1. Project supported by the National Natural Science Foundation of China (Grant No. 16931063).