Some properties of the Cauchy-type integral for the time harmonic Maxwell equations

DOI10.1007/BF01197863zbMath1020.30052OpenAlexW2019012061MaRDI QIDQ1865930

Baruch Schneider, Michael V. Shapiro

Publication date: 6 October 2003

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01197863

zbMATH Keywords

Maxwell equationsboundary valuesquaternionic analysisCauchy-type integralSokhotski-Plemelj theorem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with optics and electromagnetic theory (35Q60) Functions of hypercomplex variables and generalized variables (30G35) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Electromagnetic theory (general) (78A25)

Related Items (9)

On the Hilbert operator and the Hilbert formulas on the unit sphere for the time-harmonic Maxwell equations ⋮ Radiation conditions and integral representations for Clifford algebra-valued null-solutions of the Helmholtz operator ⋮ Some properties of the Clifford Cauchy type integrals associated to Helmholtz equation on a piecewise Lyapunov surfaces in \(\mathbb R^m\) ⋮ Cauchy representation formulas for Maxwell equations in 3-dimensional domains with fractal boundaries ⋮ Leveraging prior known vector Green functions in solving perturbed Dirac equation in Clifford algebra ⋮ The properties and iterative approximation of Cauchy-type integral operators associated with the Helmholtz equation ⋮ Boundary value problems for Dirac operators and Maxwell's equations in fractal domains ⋮ The Riemann boundary value problem related to the time-harmonic Maxwell equations ⋮ Quaternionic spherical wave functions

Cites Work

• Helmholtz operator with a quaternionic wave number and associated function theory. II: Integral representations
• Boundary value problems and Hardy spaces associated to the Helmholtz equation in Lipschitz domains
• Quaternionic time-harmonic Maxwell operator
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