L p -theory for second-order elliptic operators with unbounded coefficients

Second-order elliptic operators with unbounded coefficients of the form in are considered, which are the same as in recent papers Metafune et al. (Z Anal Anwendungen 24:497-521, 2005), Arendt et al. (J Operator Theory 55:185-211, 2006; J Math Anal Appl 338: 505-517, 2008) and Metafune et al. (Forum Math 22:583-601, 2010). A new criterion for the m-accretivity and m-sectoriality of A in is presented via a certain identity that behaves like a sesquilinear form over L (p) x L (p'). It partially improves the results in (Metafune et al. in Z Anal Anwendungen 24:497-521, 2005) and (Metafune et al. in Forum Math 22:583-601, 2010) with a different approach. The result naturally extends Kato's criterion in (Kato in Math Stud 55:253-266, 1981) for the nonnegative selfadjointness to the case of p not equal 2. The simplicity is illustrated with the typical example in which is dealt with in (Arendt et al. in J Operator Theory 55:185-211, 2006; Arendt et al. in J Math Anal Appl 338: 505-517, 2008).