Frequency Explicit Regularity Estimates for the Electric Field Integral Operator
Lehel Banjai and Stefan A. Sauter
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Submission date: 30. Jul. 2012
MSC-Numbers: 35J25, 35B65, 78A45, 65N38, 65R20
Keywords and phrases: Electromagnetic scattering, electric field integral equation, regularity of solutions
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In this paper, we derive regularity estimates for the electric field integral operator which arises when formulating the time-harmonic Maxwell problem as a boundary integral equation. More precisely, we show that the regularity constants can be bounded polynomially in terms of the frequency, where the degree of the polynomial depends on the regularity order and is given explicitly. The paper concludes with an application of these results to the electric field integral equation with distributional right-hand side.