Cores for Feller semigroups with an invariant measure

Let be an elliptic differential operator with unbounded coefficients on and assume that the associated Feller semigroup (T(t))t 0 has an invariant measure μ. Then (T(t))t 0 extends to a strongly continuous semigroup (Tp(t))t 0 on for every 1 p<∞. We prove that, under mild conditions on the coefficients of A, the space of test functions is a core for the generator (Ap,Dp) of (Tp(t))t 0 in Lp(μ) for 1 p<∞.