Feller Generators with Measure-valued Drifts

We construct a L p -strong Feller process associated with the formal differential operator − Δ + σ ⋅∇ on ℝ d , d ≥ 3 , with drift σ in a wide class of measures (e.g. the sum of a measure having density in weak L d space and a Kato class measure), by exploiting a quantitative dependence of the smoothness of the domain of an operator realization of − Δ + σ ⋅∇ generating a holomorphic C 0 -semigroup on L p ( ℝ d ) , p > d − 1, on the value of the relative bound of σ .