Maximal regularity in $L^p(\Bbb R^N)$ for a class of elliptic operators with unbounded coefficients

Abstract

Strongly elliptic differential operators with (possibly) unbounded lower-order coefficients are shown to generate $C_0$ semigroups on $L^p(\mathbb R^N)$, $1 < p < +\infty$. An explicit characterization of the domain is given.