ABSTRACT
In Chapter 9 we have seen that the Ornstein-Uhlenbeck semigroup is neither analytic nor strongly continuous in BUC(RN ). In this chapter we deal with Markov semigroups associated with the operator A defined on smooth functions by
Au(x) = ∆u(x) + N∑
bj(x)Dju(x), x ∈ R N , (10.0.1)
where bj (j = 1, . . . , N) are unbounded Lipschitz continuous functions in RN . We provide conditions on b = (b1, . . . , bN) implying that {T (t)} is not analytic in Cb(R
N ). Next, we consider the semigroup {T (t)} in Lp(RN , µ) (µ being the invariant measure associated with the operator A) and we still provide suitable growth conditions on b implying that {T (t)} is not analytic in Lp(RN , µ). The results of this chapter are taken from [117].
