Sectorialness of Second Order Elliptic Operators in Divergence Form

Abstract

A sectorial estimate is given to second order linear elliptic differential operators of divergence form. The estimate is a slight improvement of Pazy’s. The obtained constant depends on $p$ of the space ${L^p}(\Omega )(1 < p < \infty )$ and does not depend on the operators themselves. The same constant has appeared in the sectorial estimate for second order linear ordinary differential operators due to Fattorini. The result is in connection with Stein’s estimate of the analytic semigroups generated by linear elliptic differential operators.