Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable determination of sound-hard polyhedral scatterers by a minimal
  number of scattering measurements   The aim of the paper is to establish optimal stability estimates for the
determination of sound-hard polyhedral scatterers in $\mathbb{R}^N$, $N \geq
2$, by a minimal number of far-field measurements. This work is a significant
and highly nontrivial extension of the stability estimates for the
determination of sound-soft polyhedral scatterers by far-field measurements,
proved by one of the authors, to the much more challenging sound-hard case.
  The admissible polyhedral scatterers satisfy minimal a priori assumptions of
Lipschitz type and may include at the same time solid obstacles and screen-type
components. In this case we obtain a stability estimate with $N$ far-field
measurements. Important features of such an estimate are that we have an
explicit dependence on the parameter $h$ representing the minimal size of the
cells forming the boundaries of the admissible polyhedral scatterers, and that
the modulus of continuity, provided the error is small enough with respect to
$h$, does not depend on $h$. If we restrict to $N=2,3$ and to polyhedral
obstacles, that is to polyhedra, then we obtain stability estimates with fewer
measurements, namely first with $N-1$ measurements and then with a single
measurement. In this case the dependence on $h$ is not explicit anymore and the
modulus of continuity depends on $h$ as well.

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The categories of this paper are: hep-th
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph