Reconstruction of interfaces using CGO solutions for the Maxwell\n equations

2013/10/24 by Manas Kar, Kar, Manas, Mourad Sini +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1310.6577

openalex publication_date 2013/10/24 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We deal with the problem of reconstructing interfaces using complex\ngeometrical optics solutions for the Maxwell system. The contributions are\ntwofold. First, we justify the enclosure method for the impenetrable obstacle\ncase avoiding any assumption on the directions of the phases of the CGO's (or\nthe curvature of obstacle's surface). In addition, we need only a Lipschitz\nregularity of this surface. The analysis is based on some fine properties of\nthe corresponding layer potentials in appropriate Sobolev spaces. Second, we\njustify this method also for the penetrable case, where the interface is\nmodeled by the jump (or the discontinuity) of the magnetic permeability \μ.\nA key point of the analysis is the global L^p-estimates for the curl of the\nsolutions of the Maxwell system with discontinuous coefficients. These\nestimates are justified here for p near 2 generalizing to the Maxwell's\ncase the well known Meyers's L^p estimates of the gradient of the solution of\nscalar divergence form elliptic problems.\n

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• Singularities of Maxwell interface problems
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