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Clifford algebras and Maxwell's equations in Lipschitz domains
Author(s) -
McIntosh Alan,
Mitrea Marius
Publication year - 1999
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199912)22:18<1599::aid-mma95>3.0.co;2-m
Subject(s) - lipschitz continuity , mathematics , maxwell's equations , mathematical proof , clifford algebra , lipschitz domain , simple (philosophy) , boundary value problem , maxwell relations , mathematical analysis , algebra over a field , pure mathematics , inhomogeneous electromagnetic wave equation , geometry , physics , electromagnetic field , quantum mechanics , philosophy , epistemology , optical field
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. Copyright © 1999 John Wiley & Sons, Ltd.