Local H?lder Continuity Property of the Densities of Solutions of SDEs with Singular Coefficients

摘要

We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H?lder continuous drift has a H?lder continuous density function. This result complements recent results of Fournier-Printems (Bernoulli 16(2):343-360, 2010), where the density is shown to exist if both coefficients are H?lder continuous, and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion.