2025/12/08 by Xiang, Jianli, Hu, Guanghui
Mathematics · Engineering · #Numerical methods in inverse problems #Microwave Imaging and Scattering Analysis #Spectral Theory in Mathematical Physics
paper · doi:10.48550/arxiv.2512.07440
We study time harmonic scattering problems in linear elasticity in ℝ2. 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 Lamé operator and also provides an alternative idea for treating inverse elastic medium problems with a general polygonal support.