Recovery of the singularities of a potential from fixed angle scattering data

Authors
Ruiz, A
Citation
A. Ruiz, Recovery of the singularities of a potential from fixed angle scattering data, COMM PART D, 26(9-10), 2001, pp. 1721-1738
Citations number
28
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN journal
03605302 → ACNP
Volume
26
Issue
9-10
Year of publication
2001
Pages
1721 - 1738
Database
ISI
SICI code
0360-5302(2001)26:9-10<1721:ROTSOA>2.0.ZU;2-H
Abstract
We study the inverse scattering problem for Schroedinger equation. We prove that for non-smooth potential the main singularities of the potential are contained in the Born approximation which can be obtained from measurement of the scattering amplitude in a single outgoing direction. We measure sing ularities in the scale of Sobolev spaces.