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

We study Lp-theory of second-order elliptic divergence-type operators with measurable coefficients. To this end, we introduce a new method of constructing positive C0-semigroups on Lp associated with sesquilinear (not necessarily sectorial) forms in L2. A precise condition ensuring that the elliptic operator is associated with a quasi-contractive C0-semigroup on Lp is established.