The regular part of second-order differential sectorial forms with lower-order terms

TL;DR

This paper derives a formula for the regular part of sectorial forms representing second-order differential expressions with lower-order terms, revealing new behaviors introduced by these terms and characterizing when the singular part remains sectorial.

Contribution

It provides a new formula for the regular part of sectorial forms with lower-order terms, extending previous results and analyzing the impact of lower-order terms on sectoriality.

Findings

The regular part is again a differential sectorial form.

Lower-order terms introduce new behaviors.

Characterization of sectoriality of the singular part.

Abstract

We present a formula for the regular part of a sectorial form that represents a general linear second-order differential expression that may include lower-order terms. The formula is given in terms of the original coefficients. It shows that the regular part is again a differential sectorial form and allows to characterise when also the singular part is sectorial. While this generalises earlier results on pure second-order differential expressions, it also shows that lower-order terms truly introduce new behaviour.