Scattering of plane waves and a modified Pompeiu criterion

Narek Hovsepyan; Michael S. Vogelius

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arXiv · 2610.30329

Scattering of plane waves and a modified Pompeiu criterion

Narek Hovsepyan·Michael S. Vogelius

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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.

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Narek Hovsepyan, Michael S. Vogelius. 2026-10-21. Scattering of plane waves and a modified Pompeiu criterion. https://arxiv.org/abs/2610.30329

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