Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity results for transmission problems with sign-changing
  coefficients: a modal approach   We investigate some scalar transmission problems between a classical positive
material and a negative one, whose physical coefficients are negative. First,
we consider cases where the negative inclusion is a disk in 2d and a ball in
3d. Thanks to asymptotics of Bessel functions (validated numerically), we show
well-posedness but with some possible loses of regularity of the solution
compared to the classical case of transmission problems between two positive
materials. Noticing that the curvature plays a central role, we then explore
the case of flat interfaces in the context of waveguides. In this case, the
transmission problem can also have some loses of regularity, or even be
ill-posed (kernel of infinite dimension).

17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga