The Dichotomy of Forms and Operators and the Role of Green’s Forms

Bernhelm Booß-Bavnbek (), Yihan Ji (), Alessandro Portaluri () and Chaofeng Zhu ()
Additional contact information
Bernhelm Booß-Bavnbek: Roskilde University, Department of Sciences and Environment
Yihan Ji: Nankai University, Chern Institute of Mathematics and Laboratory of Pure Mathematics and Combinatorics (LPMC)
Alessandro Portaluri: Università degli studi di Torino, Dipartimento di Scienze Agrarie, Forestali e Alimentari - DISAFA
Chaofeng Zhu: Nankai University, Chern Institute of Mathematics and Laboratory of Pure Mathematics and Combinatorics (LPMC)

A chapter in Trails in Modern Theoretical and Mathematical Physics, 2023, pp 53-70 from Springer

Abstract: Abstract We consider a sesquilinear form on sections of a Hermitian bundle over a (not necessarily compact) smooth Riemannian manifold with boundary. We assume that in local coordinates, the form can be written as the integral of the inner product of differential expressions of the sections. We assign a linear operator to the form and show that it is a uniquely determined differential operator. We prove the existence and uniqueness of a differential operator on the boundary which makes a variant of Green’s formula hold.

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-44988-8_5

Ordering information: This item can be ordered from
http://www.springer.com/9783031449888

DOI: 10.1007/978-3-031-44988-8_5

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().