Reconstruction of interfaces using CGO solutions for the Maxwell equations
-
Manas Kar
and
Mourad Sini
Abstract.
We deal with the problem of reconstructing interfaces using complex geometrical optics solutions for the Maxwell system. The contributions are twofold. First, we justify the enclosure method for the impenetrable obstacle case avoiding any assumption on the directions of the phases of the CGOs (or the curvature of obstacle's surface). In addition, we need only a Lipschitz regularity of this surface. The analysis is based on some fine properties of the corresponding layer potentials in appropriate Sobolev spaces. Second, we justify this method also for the penetrable case, where the interface is modeled by the jump (or the discontinuity) of the magnetic permeability μ. A key point of the analysis is the global Lp-estimates for the curl of the solutions of the Maxwell system with discontinuous coefficients. These estimates are justified here for p near 2 generalizing to the Maxwell case the well-known Meyers's Lp-estimates of the gradient of the solution of scalar divergence form elliptic problems.
Funding source: Austrian Science Fund (FWF)
Award Identifier / Grant number: P22341-N18
© 2014 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
Articles in the same Issue
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
