Work

A Schiffer-type inverse obstacle problem for the planar Schrödinger equation with a single measurement

Year: 2026

Type: preprint

Abstract: We prove a single measurement uniqueness result for interior sound-soft obstacles in the planar Schrödinger equation with an unknown surrounding potential. For any two configurations with different obstacles, we construct a boundary datum for which the corresponding Neumann measurements differ. The full Dirichlet-to-Neumann map uniquely determines both the obstacle and the potential. The obstacles may have several connected components, and no convexity or analyticity assumptions are imposed. Neither potential is required to be known near the measurement boundary.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.12206

Authors: Liimatainen, Tony, Lin, Yi-Hsuan, Ola, Petri

Institution: University of Helsinki

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Alexander von Humboldt-Stiftung, Universität Duisburg-Essen, National Science and Technology Council

OpenAlex ID: W7221195400

Cites: 5

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Related to: 10