Clifford Algebras and Maxwell's Equations in Lipschitz Domains

Alan McIntosh; Marius Mitrea

doi:10.1002/(SICI)1099-1476(199912)22:18<1599::AID-MMA95>3.0.CO;2-M

Clifford Algebras and Maxwell's Equations in Lipschitz Domains

Alan McIntosh^*, Marius Mitrea

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

54 Citations (Scopus)

Abstract

We present a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of ℝ^m. Among other things, we give new proofs to the boundary energy estimates of Rellich type for Maxwell's equations in Lipschitz domains from [20, 10], discuss radiation conditions and the case of variable wave number.

Original language	English
Pages (from-to)	1599-1620
Number of pages	22
Journal	Mathematical Methods in the Applied Sciences
Volume	22
Issue number	18
DOIs	https://doi.org/10.1002/(SICI)1099-1476(199912)22:18<1599::AID-MMA95>3.0.CO;2-M
Publication status	Published - Dec 1999

Access to Document

10.1002/(SICI)1099-1476(199912)22:18<1599::AID-MMA95>3.0.CO;2-M

Cite this

@article{aab97edaa2ea420e8f5a5c867b62ba89,

title = "Clifford Algebras and Maxwell's Equations in Lipschitz Domains",

abstract = "We present a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of ℝm. Among other things, we give new proofs to the boundary energy estimates of Rellich type for Maxwell's equations in Lipschitz domains from [20, 10], discuss radiation conditions and the case of variable wave number.",

keywords = "Clifford algebras, Hardy spaces, Lipschitz domains, Maxwell's equations, Radiation conditions, Rellich identities",

author = "Alan McIntosh and Marius Mitrea",

year = "1999",

month = dec,

doi = "10.1002/(SICI)1099-1476(199912)22:18<1599::AID-MMA95>3.0.CO;2-M",

language = "English",

volume = "22",

pages = "1599--1620",

journal = "Mathematical Methods in the Applied Sciences",

issn = "0170-4214",

publisher = "John Wiley & Sons Ltd.",

number = "18",

}

TY - JOUR

T1 - Clifford Algebras and Maxwell's Equations in Lipschitz Domains

AU - McIntosh, Alan

AU - Mitrea, Marius

PY - 1999/12

Y1 - 1999/12

N2 - We present a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of ℝm. Among other things, we give new proofs to the boundary energy estimates of Rellich type for Maxwell's equations in Lipschitz domains from [20, 10], discuss radiation conditions and the case of variable wave number.

AB - We present a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of ℝm. Among other things, we give new proofs to the boundary energy estimates of Rellich type for Maxwell's equations in Lipschitz domains from [20, 10], discuss radiation conditions and the case of variable wave number.

KW - Clifford algebras

KW - Hardy spaces

KW - Lipschitz domains

KW - Maxwell's equations

KW - Radiation conditions

KW - Rellich identities

UR - http://www.scopus.com/inward/record.url?scp=0000802210&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1099-1476(199912)22:18<1599::AID-MMA95>3.0.CO;2-M

DO - 10.1002/(SICI)1099-1476(199912)22:18<1599::AID-MMA95>3.0.CO;2-M

M3 - Article

SN - 0170-4214

VL - 22

SP - 1599

EP - 1620

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 18

ER -

Clifford Algebras and Maxwell's Equations in Lipschitz Domains

Abstract

Access to Document

Other files and links

Fingerprint

Cite this