Maximal sector of analyticity for $C_{0}$-semigroups generated by elliptic operators with separation property in $L^{p}$
Giorgio Metafune, Noboru Okazawa, Motohiro Sobajima, Tomomi Yokota · Università del Salento · 2013
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{ abla}u) + (F\cdot{ abla})u + Vu$ and the lower order coefficients have singularities at infinity or at the origin.