2023/10/09 by Luca Rondi, Rondi, Luca
Engineering · Mathematics · Physics and Astronomy · #35R30 #Analysis of PDEs (math.AP) #Electromagnetic Scattering and Analysis #FOS: Mathematics #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2310.05581
openalex publication_date 2023/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique continuation and a suitable reflection principle are enough to proceed with the constructions, without any other assumption on the underlying partial differential equation or the boundary condition. We also aim to keep the geometric constructions and their proofs as simple as possible. To illustrate the applicability of this theory, we show how several uniqueness results present in the literature immediately follow from our arguments. Indeed we believe that this theory may serve as a roadmap for establishing similar uniqueness results for other partial differential equations or boundary conditions.