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arXiv · 1811.03443

Uniqueness for the inverse fixed angle scattering problem

Juan A. Barceló·Carlos Castro·Teresa Luque·Cristóbal J. Meroño·Alberto Ruiz·María de la Cruz Vilela
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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 $β>2/3$.

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Juan A. Barceló, Carlos Castro, Teresa Luque, Cristóbal J. Meroño, Alberto Ruiz, María de la Cruz Vilela. 2019-03-18. Uniqueness for the inverse fixed angle scattering problem. https://arxiv.org/abs/1811.03443

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