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arXiv · 2512.07440

Absence of the analytic continuation of elastic transmission eigenfunctions at rectangular corners

Jianli Xiang·Guanghui Hu
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Abstract

We study time harmonic scattering problems in linear elasticity in $\mathbb{R}^{2}$. We show that certain penetrable scatterers with rectangular corners scatter every incident wave nontrivially. Even though these scatterers have interior transmission eigenvalues, the far field operator has a trivial kernel at every real frequency. Our approach relies on a special decomposition of the elastic Lam\'e operator and also provides an alternative idea for treating inverse elastic medium problems with a general polygonal support.

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Jianli Xiang, Guanghui Hu. 2025-12-08. Absence of the analytic continuation of elastic transmission eigenfunctions at rectangular corners. https://arxiv.org/abs/2512.07440

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