Work

Scattering of plane waves and a modified Pompeiu criterion

Year: 2026

Type: preprint

Abstract: In this paper we prove that plane waves always scatter from bounded, strictly convex planar inhomogeneities with constant material parameters. Our approach involves the introduction of a modified Pompeiu property, whose failure corresponds to the vanishing of the Fourier transform of the indicator function of the inhomogeneity on a complexified circle not centered at the origin. We then show that such vanishing is impossible for bounded, strictly convex planar sets.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.30329

Authors: Hovsepyan, Narek, Vogelius, Michael S.

Institutions: The University of Texas Rio Grande Valley, Rutgers, The State University of New Jersey

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7223327887

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