Jump to ContentJump to Main Navigation
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics$
Users without a subscription are not able to see the full content.

G. F. Roach, I. G. Stratis, and A. N. Yannacopoulos

Print publication date: 2012

Print ISBN-13: 9780691142173

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142173.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 13 December 2017

Spaces and Operators

Spaces and Operators

Chapter:
(p.38) Chapter Three Spaces and Operators
Source:
Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics
Author(s):

G. F. Roach

I. G. Stratis

A. N. Yannacopoulos

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142173.003.0003

This chapter consists mainly of definitions and various properties (without proofs) of spaces and operators used in this book. It defines O as an open set in Rᶰ such that it is locally on one side of its boundary Γ‎ := δ‎O, which is supposed to be bounded and Lipschitz. The chapter is mainly focused on the case of N = 3. Further, without loss of generality, the chapter supposes that Γ‎ is connected (for otherwise, one could work separately at each connected component). Such a set O is referred to as ‘regular’ in what follows. Let n denote the outward unit normal vector to Γ‎. In addition, let Oₑ := Rᶰ∖Ō: By N₀ we denote the set N ∪ {0}.

Keywords:   spaces, operators, function spaces, standard differential, trace operators, decompositions, compact embeddings, vector analysis, Maxwell operator

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.