Local H\"{o}lder continuity property of the Densities of Solutions of   SDEs with Singular Coefficients
  We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H\"{o}lder continuous drift has a H\"{o}lder continuous density function. This result complements recent results of Fournier-Printems \cite{F1}, where the density is shown to exist if both coefficients are H\"{o}lder continuous and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion. 
Masafumi Hayashi, Arturo Kohatsu-Higa and Go Yuki
math.PR