Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shape differentiability of Helmholtz scattering problems via explicit
  shape calculus   We consider the time-harmonic scalar wave scattering problems with Dirichlet,
Neumann, impedance and transmission boundary conditions. Under this setting, we
analyze how sensitive diffracted fields and Cauchy data are to small
perturbations of a given nominal shape. To this end, we follow [K. Eppler,
Int.~J.~Appl. Math. Comput. Sci. 10(3) (2000), pp. 487-516], referred to as
explicit shape calculus, and which places great emphasis on the
characterization of the domain derivatives as boundary value problems. It
consists in combining elliptic regularity theorems, shape calculus and
functional analysis, allowing to deduce sharp differentiability results for the
domain-to-solution and domain-to-Cauchy data mappings. The technique is applied
to both classic and limit Sobolev regularity cases, leading to new and
comprehensive differentiability results.

26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph