The Holder and the Besov regularity of the density for the solution of a parabolic stochastic partial differential equation

In this paper we prove that the density p(t,x)(y) of the solution of a whit e-noise-driven parabolic stochastic partial differential equation (SPDE) sa tisfying a strong ellipticity condition is 1/2 Lipschitz continuous with re spect to (w.r.t.) t and 1-epsilon Lipschitz continuous w.r.t. x for all eps ilon is an element of ]0, 1[. In addition, we show that it belongs to the B esov space B-1,B-infinity,B-infinity w.r.t. x. The proof is based on the Ma lliavin calculus of variations and on some refined estimates for the Green kernel associated with the SPDE.