Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cloaking property of a plasmonic structure in doubly complementary media
  and three-sphere inequalities with partial data   We investigate cloaking property of negative-index metamaterials in the
time-harmonic electromagnetic setting for the so-called doubly complementary
media. These are media consisting of negative-index metamaterials in a shell
(plasmonic structure) and positive-index materials in its complement for which
the shell is complementary to a part of the core and a part of the exterior of
the core-shell structure. We show that an arbitrary object is invisible when it
is placed close to a plasmonic structure of a doubly complementary medium as
long as its cross section is smaller than a threshold given by the property of
the plasmonic structure. To handle the loss of the compactness and of the
ellipticity of the modeling Maxwell equations with sign-changing coefficients,
we first obtain Cauchy's problems associated with two Maxwell systems using
reflections. We then derive information from them, and combine it with the
removing localized singularity technique to deal with the localized resonance.
A central part of the analysis on the Cauchy's problems is to establish
three-sphere inequalities with partial data for general elliptic systems, which
are interesting in themselves. The proof of these inequalities first relies on
an appropriate change of variables, inspired by conformal maps, and is then
based on Carleman's estimates for a class of degenerate elliptic systems.

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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an