Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shape derivatives of boundary integral operators in electromagnetic
  scattering. Part II : Application to scattering by a homogeneous dielectric
  obstacle   We develop the shape derivative analysis of solutions to the problem of
scattering of time-harmonic electromagnetic waves by a bounded penetrable
obstacle. Since boundary integral equations are a classical tool to solve
electromagnetic scattering problems, we study the shape differentiability
properties of the standard electromagnetic boundary integral operators. The
latter are typically bounded on the space of tangential vector fields of mixed
regularity $TH\sp{-1/2}(\Div_{\Gamma},\Gamma)$. Using Helmholtz decomposition,
we can base their analysis on the study of pseudo-differential integral
operators in standard Sobolev spaces, but we then have to study the G\^ateaux
differentiability of surface differential operators. We prove that the
electromagnetic boundary integral operators are infinitely differentiable
without loss of regularity. We also give a characterization of the first shape
derivative of the solution of the dielectric scattering problem as a solution
of a new electromagnetic scattering problem.

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The categories of this paper are: astro-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin