Electromagnetic Steklov eigenvalues: approximation analysis

We continue the work of Camano et al . [ SIAM J. Math. Anal. 49 (2017) 4376–4401] on electromagnetic Steklov eigenvalues. The authors recognized that in general eigenvalues do not correspond to spectrum a compact operator and hence proposed modified eigenvalue problem with desired properties. present article considers original problem. cast problems as for holomorphic function A (?). construct “test function” T (?) so ( ? ) is weakly )-coercive all suitable , i.e. )* perturbation coercive operator. construction relies decomposition space into subspaces an apt sign change each subspace. For approximation analysis, we apply framework T-compatible Galerkin approximations. problem, prove convenient commuting projection operators imply T-compatibility convergence. require satisfy additional commutator property which concerns tangential trace. existence such remain open questions.