H\"{o}lder Continuity of the Solution for a Class of Nonlinear SPDE   Arising from One Dimensional Superprocesses
  The H\"older continuity of the solution to a nonlinear stochastic partial differential equation arising from one dimensional super process is obtained. It is proved that the H\"older exponent in time variable is as close as to 1/4, improving the result of 1/10 in a recent paper by Li et al [3]. The method is to use the Malliavin calculus. The H\"older continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This H\"older continuity result is sharp since the corresponding linear heat equation has the same H\"older continuity. 
Yaozhong Hu, Fei Lu and David Nualart
math.PR math.AP