Recent Advances in L p -Theory of Homotopy Operator on Differential Forms

Abstract

The purpose of this survey paper is to present an up-to-date account of the recent advances made in the study of $L^p$-theory of the homotopy operator applied to differential forms. Specifically, we will discuss various local and global norm estimates for the homotopy operator T and its compositions with other operators, such as Green’s operator and potential operator.