Calderón problem for Maxwell's equations in cylindrical domain

Oleg Yu. Imanuvilov; Masahiro Yamamoto

doi:10.3934/ipi.2014.8.1117

Article Contents

2014, Volume 8, Issue 4: 1117-1137. Doi: 10.3934/ipi.2014.8.1117

This issue Previous Article An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method Next Article Increasing stability for determining the potential in the Schrödinger equation with attenuation from the Dirichlet-to-Neumann map

Calderón problem for Maxwell's equations in cylindrical domain

Oleg Yu. Imanuvilov^1, and
Masahiro Yamamoto^2,

1.
Department of Mathematics, Colorado State University,101 Weber Building, Fort Colins, CO 80523-1784
2.
Department of Mathematical Sciences, The University of Tokyo, Komaba Meguro Tokyo 153-8914

Received: December 2013

Revised: September 2014

Published online: November 2014

Abstract / Introduction Related Papers Cited by

Abstract

We prove some uniqueness results in determination of the conductivity, the permeability and the permittivity of Maxwell's equations in a cylindrical domain $\Omega \times (0,L)$ from partial boundary map. More specifically, for an arbitrarily given subboundary $\Gamma_0 \subset \partial\Omega$, we prove that the coefficients of Maxwell's equations can be uniquely determined in the subdomain $(\Omega \setminus$ [the convex hull of $\Gamma_0])$ $ \times (0,L)$ by the boundary map only for inputs vanishing on $\Gamma_0 \times (0,L)$.

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Mathematics Subject Classification: Primary: 35R30, 35F35; Secondary: 35Q61.

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