In this paper we prove that the density of the solution of a white-noise-driven parabolic stochastic partial differential equation (SPDE) satisfying a strong ellipticity condition is Lipschitz continuous with respect to (w.r.t.) and Lipschitz continuous w.r.t. for all . In addition, we show that it belongs to the Besov space w.r.t. . The proof is based on the Malliavin calculus of variations and on some refined estimates for the Green kernel associated with the SPDE.
"The Hölder and the Besov regularity of the density for the solution of a parabolic stochastic partial differential equation." Bernoulli 5 (2) 275 - 298, april 1999.