Inverse problems for screens

We study the inverse scattering from a screen with using only one incoming time-harmonic plane wave but with measurements of the scattered wave done at all directions. Especially we focus on the $(2D)$–case i.e. (inverse) scattering from an open bounded smooth curve.
Beside the inverse scattering problems we discuss also the inverse electrostatic problem. This corresponds to case where the wave number is set equal to zero. More exactly the new theorem proved in collaboration with P. Ola and E. Blåsten 2024 states that the Cauchy data on a circle $C$ of one single function $u$ that satisfies
i) $u$ is bounded and harmonic outside the screen $\Gamma\in\mathbb{R}^2$
ii) $u$ is continuous in $\mathbb{R}^2$ and vanishes on $\Gamma$
is enough to determine $\Gamma$ uniquely.