2022/07/13 by Martin Halla, Halla, Martin
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2207.06498
openalex publication_date 2022/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent decades qualitative inverse scattering methods with eigenvalues as target signatures received much attention. To understand those methods a knowledge on the properties of the related eigenvalue problems is essential. However, even the existence of eigenvalues for such (nonselfadjoint) problems is a challenging question and existing results for absorbing media are usually established under unrealistic assumptions or a smoothing of the eigenvalue problem. We present a technique to prove the existence of infinitely many eigenvalues for such problems under realistic assumptions. In particular we consider the class of scalar and modified Maxwell nonselfadjoint Steklov eigenvalue problems. In addition, we present stability results for the eigenvalues with respect to changes in the material parameters. In distinction to existing results the analysis of the present article requires only minimal regularity assumptions. By that we mean that the regularity of the domain is not required to be better than Lipschitz, and the material coefficients are only assumed to be piece-wise W1,∞. Also the stability estimates for eigenvalues are obtained solely in Lp-norms (p<∞) of the material perturbations.