On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra

Authors
Buffa, A Ciarlet, P
Citation
A. Buffa et P. Ciarlet, On traces for functional spaces related to Maxwell's equations Part I: An integration by parts formula in Lipschitz polyhedra, MATH METH A, 24(1), 2001, pp. 9-30
Citations number
24
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
ISSN journal
01704214 → ACNP
Volume
24
Issue
1
Year of publication
2001
Pages
9 - 30
Database
ISI
SICI code
0170-4214(20010110)24:1<9:OTFFSR>2.0.ZU;2-L
Abstract
The aim of this paper is to study the tangential trace and tangential compo nents of fields which belong to the space H(curl, Omega), when Omega is a p olyhedron with Lipschitz continuous boundary. The appropriate functional se tting is developed in order to suitably define these traces on the whole bo undary and on a part of it (for partially vanishing fields and general ones .) In both cases it is possible to define ad hoc dualities among tangential trace and tangential components. In addition, the validity of two related integration by parts formulae is provided. Copyright (C) 2001 John Wiley & Sons, Ltd.