2020/06/29 by Samuel Cogar, Cogar, Samuel
Engineering · Mathematics · #35J25 #35P05 #35P25 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geophysical Methods and Applications #Numerical methods in engineering #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2006.16428
openalex publication_date 2020/06/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
A recent area of interest is the development and study of eigenvalue problems\narising in scattering theory that may provide potential target signatures for\nuse in nondestructive testing of materials. We consider a generalization of the\nelectromagnetic Stekloff eigenvalue problem that depends upon a smoothing\nparameter, for which we establish two main results that were previously\nunavailable for this type of eigenvalue problem. First, we use the theory of\ntrace class operators to prove that infinitely many eigenvalues exist for a\nsufficiently high degree of smoothing, even for an absorbing medium. Second, we\nleverage regularity results for Maxwell's equations in order to establish\nstability results for the eigenvalues with respect to the material\ncoefficients, and we show that this generalized class of Stekloff eigenvalues\nconverges to the standard class as the smoothing parameter approaches zero.\n