Harmonic Analysis of Dirac Operators on Lipschitz Domains

Axelsson, Andreas; Grognaxd, René; Hogan, Jeffrey A.; McIntosh, Alan

doi:10.1007/978-94-010-0862-4_22

Cited by 27 publications

(38 citation statements)

References 14 publications

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“…In particular, this holds true for the electromagnetic ÿeld F described in Example 1.1 below. This approach to Maxwell's equations, using the elliptic Dirac operator D k , builds on earlier works by McIntosh and Mitrea [1] and Axelsson et al [2].…”

Section: Introductionmentioning

confidence: 97%

Transmission problems for Maxwell's equations with weakly Lipschitz interfaces

Axelsson

2006

Math. Meth. Appl. Sci.

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SUMMARYWe prove su cient conditions on material constants, frequency and Lipschitz regularity of interface for well posedness of a generalized Maxwell transmission problem in ÿnite energy norms. This is done by embedding Maxwell's equations in an elliptic Dirac equation, by constructing the natural trace space for the transmission problem and using Hodge decompositions for operators d and on weakly Lipschitz domains to prove stability. We also obtain results for boundary value problems and transmission problems for the Hodge-Dirac equation and prove spectral estimates for boundary singular integral operators related to double layer potentials.

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Section: Introductionmentioning

confidence: 97%

Transmission problems for Maxwell's equations with weakly Lipschitz interfaces

Axelsson

2006

Math. Meth. Appl. Sci.

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“…The first step is the calculation of f + and f − on the surface Σ in whole field Clifford form (see table I in [12]). The second step is the extension of those fields away from the boundary using the Cauchy extension formula [13,14]:…”

Section: Solutionmentioning

confidence: 99%

An EM scattering algorithm for all materials

Seagar

Chantaveerod

2015

2015 International Conference on Electromagnetics in Advanced Applications (ICEAA)

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“…For more background material and further general references, the interested reader is referred to monographs [6][7][8][9][10][11]; see also the articles [12][13][14][15], for harmonic and Fourier analysis methods in the context of Cli ord algebras. An excellent survey of progress in the area of harmonic analysis techniques for non-smooth elliptic problems until early 1990s can be found in Reference [16].…”

Section: Theorem 11mentioning

confidence: 99%