“Steklov eigenvalues for Maxwell’s equations”
Mercoledì 25 Novembre 2020, ore 17.00 - Zoom - Samuel Cogar (Rutgers University - USA)
A recent area of interest has been the development of new eigenvalue problems arising from scattering theory that may be used as target signatures in nondestructive testing of materials. In this talk I will focus on the Steklov eigenvalue problem for Maxwell’s equations. After motivating this area of research with the simpler Steklov eigenvalue problem for the Helmholtz equation, I will introduce the time-harmonic Maxwell’s equations and give some background on their study. The corresponding Steklov problem will then be described, including the modified versions that have been devised to correct some degenerate behavior in the eigenvalues. I will conclude with a further modification of my own for which infinitely many Steklov eigenvalues exist without any additional assumptions on the coefficients, a result that is not available for other classes of Steklov eigenvalues.