On the Lp-Theory of C0-Semigroups Associated with Second-Order Elliptic Operators, II

We study positive C0-semigroups on Lp associated with second-order uniformly elliptic divergence-type operators with singular lower-order terms, subject to a wide class of boundary conditions. We obtain an interval (pmin, pmax) in the Lp-scale where these semigroups can be defined, including the case 2∉(pmin, pmax). We present an example showing that the result is optimal. We also show that the semigroups are analytic with angles of analyticity and spectra of the generators independent of p, for the whole range of p where the semigroups are defined.