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

56 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

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

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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.",

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AU - Mitrea, Marius

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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 - https://www.scopus.com/pages/publications/0000802210

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

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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

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