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 $-Δ+q$, where $q$ is a small real valued potential with compact support in the Sobolev space $W^{β,2}$ with $β>0.$ 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 $W^{β,2}$ with $β>2/3$.