A new approach to the Lᵖ-theory of -Δ+ b·∇, and its applications to Feller processes with general drifts

الأصل · EN

We develop a detailed regularity theory of -Δ+b·∇ in Lᵖ(Rᵈ), for a wide class of vector fields. The Lᵖ-theory allows us to construct associated strong Feller process in C∞(Rᵈ). Our starting object is an operator-valued function, which, we prove, coincides with the resolvent of an operator realization of -Δ+ b· ∇, the generator of a holomorphic C₀-semigroup on Lᵖ(Rᵈ). Then the very form of the operator-valued function yields crucial information about smoothness of the domain of the generator.