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

Abstract

An inverse problem for the two-dimensional Schrodinger equation with $L_{com}^p$-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 $v\in L_{com}^p$.

There is an inconsistency in the choice of the sign for the potential $v$ in the journal version of this paper

References in corpus (3)

• A global stability estimate for the Gel'fand-Calderon inverse problem in two dimensions
• Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
• Global solution of the initial value problem for the focusing Davey-Stewartson II system

Cited by in corpus (1)

• Reconstruction of rough potentials in the plane