Reconstruction of the singularities of a potential from backscattering data in 2D and 3D
| dc.creator | Reyes, Juan Manuel | |
| dc.creator | Ruiz, Alberto | |
| dc.date | 2009-02-18 | |
| dc.date.accessioned | 2026-07-07T12:43:31Z | |
| dc.date.available | 2026-07-07T12:43:31Z | |
| dc.description | We prove that the singularities of a potential in the two and three dimensional Schrödinger 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. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/0902.3096 | |
| dc.identifier | http://arxiv.org/abs/0902.3096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220446 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q40 | |
| dc.title | Reconstruction of the singularities of a potential from backscattering data in 2D and 3D | |
| dc.type | text |