White noise driven parabolic SPDEs with measurable drift (Q1328281)

A quasilinear SPDE driven by a space-time white noise is under consideration. Similar equations were considered recently by \textit{E. Pardoux} and \textit{T. Zhang} [ibid. 112, No. 2, 447-458 (1993; Zbl 0777.60046)] under more strong coefficients regularity assumptions. The main result states the existence and uniqueness of the strong solution under measurability assumption on the ``drift'' coefficient and a nondegeneracy and some smoothness on the ``diffusion'' coefficient along with some coefficients growth assumptions. The result is proved with the help of a priori density estimate established with the help of Malliavin calculus technique.