The spectrum of double layer potentials for some 3D domains with corners and edges

Date/heure
11 janvier 2019
11:00 - 12:00

Oratrice ou orateur
Karl-Mikael Perfekt

Catégorie d'évènement
Séminaire EDP, Analyse et Applications (Metz)

I will talk about the spectrum of double layer potential operators for 3D surfaces with rough features. The existence of spectrum reflects the fact that transmission problems across the surface may be ill-posed for (complex) sign-changing coefficients. The spectrum is very sensitive to the regularity sought of solutions. For $L^2$ boundary data, for domains with corners and edges, the spectrum is complex and carries an associated index theory. Through an operator-theoretic symmetrisation framework, it is also possible to recover the initial self-adjoint features of the transmission problem – corresponding to $H^{1/2}$ boundary data – in which case the spectral picture is more familiar.