Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cloaking using complementary media for the Helmholtz equation and a
  three spheres inequality for second order elliptic equations   Cloaking using complementary media was suggested by Lai et al. This was
proved in the quasistatic regime by H. M. Nguyen. One of the difficulties in
the study of this problem is the appearance of the localized resonance, i.e.,
the fields blow up in some regions and remain bounded in some others as the
loss goes to 0. To this end, the author introduced the technique of removing
localized singularity and used a standard three spheres inequality. This method
also works for the Helmholtz equation. However, it requires small size of the
cloaked region for large frequency due to the use of the (standard) three
spheres inequality. In this paper, we give a proof of cloaking using
complementary media in the finite frequency regime without imposing any
condition on the cloaked region; hence the cloak works for all frequency. To
successfully apply the approach of H.M. Nguyen, we establish a new three
spheres inequality. A modification of the cloaking setting to obtain illusion
optics is also discussed.

4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org