Recovery of jumps and singularities in the multidimensional Schrodinger operator from limited data

Pages: 525 - 535, Volume 1, Issue 3, August 2007

doi:10.3934/ipi.2007.1.525       Abstract        Full Text (156.2K)       Related Articles

Lassi Päivärinta - Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 FI-00014, Finland (email)
Valery Serov - Department of Mathematical Sciences, University of Oulu, Finland (email)

Abstract: The inverse scattering problem for multidimensional Schrödinger operator is studied. More exactly we prove a new formula for the first nonlinear term to estimate more accurately this term. This estimate allows to conclude that all singularities and jumps of the unknown potential can be recovered from the Born approximation. Especially, we show for the potentials in $L^p$ for certain values of $p$ that the approximation agrees with the true potential up to the continuous function.% Text of abstract

Keywords:  Inverse problems, Schrödinger operator, Born approximation.
Mathematics Subject Classification:  Primary: 81U40, 35P25.

Received: January 2007;      Published: July 2007.