Maximal sector of analyticity for $C_{0}$-semigroups generated by elliptic operators with separation property in $L^{p}$

Abstract

Analytic continuation of the $C_{0}$-semigroup $\{e^{-zA}\}$ on $L^{p}(\mathbb{R}^{N})$ generated by the second order elliptic operator $- A$ is investigated, where $A$ is formally defined by the differential expression $ Au = -{\rm div}(a{\nabla}u) + (F\cdot{\nabla})u + Vu $ and the lower order coefficients have singularities at infinity or at the origin. \end