Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On electromagnetic scattering from a penetrable corner   This article is concerned with the time-harmonic electromagnetic (EM)
scattering from a generic inhomogeneous medium. It is shown that if there is a
right corner on the support of the medium, then it scatters every pair of
incident EM fields, excluding a possible class of EM fields which are of very
particular forms. That is, for every pair of admissible incident EM fields, the
corresponding scattered wave fields associated to the medium scatterer cannot
be identically vanishing outside the support of the medium. Indeed, we achieve
the corner scattering result by establishing a stronger result, that shows the
failure of the analytic extension across the corner of certain EM fields
satisfying the so-called interior transmission eigenvalue problem. This extends
the relevant study in [3] for the acoustic scattering governed by the Helmholtz
equation to the electromagnetic case governed by the Maxwell system.
Substantial new challenges arise from the corresponding extension from the
scalar PDE to the system of PDEs. Our mathematical arguments combine the
analysis for interior transmission eigenvalue problems associated to the
Maxwell system; the derivation of novel orthogonality relation for the
solutions of Maxwell systems; the construction of complex-geometrical-optics
(CGO) solutions for the Maxwell system with new Lp-estimates (p > 6) on the
remainder terms; and the proof of the non-vanishing property for the Laplace
transform of vectorial homogeneous harmonic polynomials.

4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc