Global properties of generalized Ornstein–Uhlenbeck operators on Lp(RN,RN) with more than linearly growing coefficients

We show that the realization Ap of the elliptic operator Au=div(Q∇u)+F⋅∇u+Vu in Lp(RN,RN), p∈[1,+∞[, generates a strongly continuous semigroup, and we determine its domain if 1