Uniqueness for the inverse fixed angle scattering problem

Abstract

We present a uniqueness result in dimensions $2$ and $3$ for the inverse fixed angle scattering problem associated to the Schrödinger operator $-\Delta +q$, where $q$ is a small real valued potential with compact support in the Sobolev space $W^{\beta ,2}$ with $\beta >0.$ This result improves the known result, due to Stefanov, in the sense that almost no regularity is required for the potential. The uniqueness result still holds in dimension $4$, but for more regular potentials in $W^{\beta ,2}$ with $\beta >2/3$.