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- W4324325704 abstract "This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with boundary $partial M$ endowed with a Riemannian metric $g$. Assuming that the electric permittivity $varepsilon$ and magnetic permeability $mu$ are real-valued anisotropic (i.e $(1,1)-$ tensors), we aim to determine certain metrics induced by these parameters, denoted by $hat{varepsilon}$ and $hat{mu}$ at $partial M$. We show that the knowledge of the impedance and admittance maps determines the tangential entries of $hat{varepsilon}$ and $hat{mu}$ at $partial M$ in their boundary normal coordinates, although the background volume form cannot be determined in such coordinates due to a non-uniqueness occuring from diffeomorphisms that fix the boundary. Then, we prove that in some cases, we can also recover the normal components of $hat{mu}$ up to a conformal multiple at $partial M$ in boundary normal coordinates for $hat{varepsilon}$. Last, we build an inductive proof to show that if $hat{varepsilon}$ and $hat{mu}$ are determined at $partial M$ in boundary normal coordinates for $hat{varepsilon}$, then the same follows for their normal derivatives of all orders at $partial M$." @default.
- W4324325704 created "2023-03-16" @default.
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- W4324325704 date "2023-03-12" @default.
- W4324325704 modified "2023-10-16" @default.
- W4324325704 title "Boundary Recovery of Anisotropic Electromagnetic Parameters for the Time Harmonic Maxwell's Equations" @default.
- W4324325704 doi "https://doi.org/10.48550/arxiv.2303.06688" @default.
- W4324325704 hasPublicationYear "2023" @default.
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