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arXiv · 2209.13255

Recovery of singularities from fixed angle scattering data for biharmonic operator in dimensions two and three

Jaakko Kultima
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Abstract

The inverse fixed angle problem for operator $\Delta^2 u + V(x,|u|) u$ is considered in dimensions $n=2,3$. We prove that the difference between an inverse fixed angle Born approximation and the function $V(\cdot,1)$ is smoother than the function $V$ itself in some Sobolev scale. This allows us to conclude that the main singularities of the perturbation $V$ can be reconstructed from the knowledge of the scattering amplitude with some fixed incident angle.

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Jaakko Kultima. 2022-09-27. Recovery of singularities from fixed angle scattering data for biharmonic operator in dimensions two and three. https://arxiv.org/abs/2209.13255

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