Time-dependent diffusion operators on L

We study the Cauchy problem for time-dependent diffusion operators with singular coefficients on L-1-spaces induced by infinitesimal invariant measures. We give sufficient conditions on the coefficients such that the Cauchy-Problem is well-posed. We construct associated diffusion processes with the help of the theory of generalized Dirichlet forms. We apply our results in particular to construct a large class of Nelson-diffusions that could not been constructed before.