Inverse Problems for Screens

TL;DR

This paper investigates inverse scattering and electrostatic problems involving screens, demonstrating unique determination of the screen from limited data in 2D, with implications for inverse problems and harmonic analysis.

Contribution

It introduces new uniqueness results for inverse scattering and electrostatic problems using minimal data in the 2D case, focusing on screens and harmonic functions.

Findings

Unique determination of screens from Cauchy data.

Analysis of inverse scattering with a single incident wave.

Results applicable to harmonic functions vanishing on screens.

Abstract

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. Besides the inverse scattering problem we also study the inverse electrostatic problem. We then show that one Cauchy--data of any continuous and bounded function vanishing on the screen and harmonic outside it, determines the screen uniquely.