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Abstract and Applied Analysis
Volume 2014, Article ID 596704, 20 pages
Review Article

Recent Advances in -Theory of Homotopy Operator on Differential Forms

1Department of Mathematics, Seattle University, Seattle, WA 98122, USA
2Department of Epidemiology, Harvard University, Boston, MA 02115, USA
3Department of Mathematics, Harbin Institute of Technology, Harbin, China

Received 23 January 2014; Accepted 20 March 2014; Published 4 May 2014

Academic Editor: Yuming Xing

Copyright © 2014 Shusen Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The purpose of this survey paper is to present an up-to-date account of the recent advances made in the study of -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.