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arXiv · 1608.05807

Recovery of $L^p$-potential in the plane

Evgeny Lakshtanov·Boris Vainberg
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Abstract

An inverse problem for the two-dimensional Schrodinger equation with $L^p_{com}$-potential, $p>1$, is considered. Using the $\overline{\partial}$-method, the potential is recovered from the Dirichlet-to-Neumann map on the boundary of a domain containing the support of the potential. We do not assume that the potential is small or that the Faddeev scattering problem does not have exceptional points. The paper contains a new estimate on the Faddeev Green function that immediately implies the absence of exceptional points near the origin and infinity when $v\in L^p_{com}$.

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Evgeny Lakshtanov, Boris Vainberg. 2017-02-19. Recovery of $L^p$-potential in the plane. https://doi.org/10.1515/jiip-2016-0052

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