Vi. Bogachev et al., REGULARITY OF INVARIANT-MEASURES - THE CASE OF NONCONSTANT DIFFUSION PART, Journal of functional analysis, 138(1), 1996, pp. 223-242
We prove regularity (i.e., smoothness) of measures mu on R(d) satisfyi
ng the equation Lmu = 0 where L is an operator of type Lu = tr(Au-'')
+ B . del u. Here A is a Lipschitz continuous, uniformly elliptic mat
rix-valued map and B is merely mu-square integrable. We also treat a c
lass of corresponding infinite dimensional cases where R(d) is replace
d by a locally convex topological vector space X. In this cases mu is
proved to be absolutely continuous w.r.t. a Gaussian measure on X and
the square root of the Radon-Nikodym density belongs to the Malliavin
test function space D-2,D-1. (C) 1996 Academic Press. Inc.