Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reconstruction of the singularities of a potential from backscattering
  data in 2D and 3D   We prove that the singularities of a potential in the two and three
dimensional Schr\"odinger equation are the same as the singularities of the
Born approximation (Diffraction Tomography), obtained from backscattering
inverse data, with an accuracy of $1/2^-$ derivative in the scale of
$L^2$-based Sobolev spaces. The key point is the study of the smoothing
properties of the quartic term in the Neumann-Born expansion of the scattering
amplitude in 3D, together with a Leibniz formula for multiple scattering valid
in any dimension.

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The categories of this paper are: cs
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc