Functional Analysis and Applications Seminar 

02/10/2009, 15:00 — 16:00 — Room P3.10, Mathematics Building
Roland Duduchava, Andrea Razmadze Mathematical Institute and IB Euro-Caucasian University, Tbilisi, Georgia

Equivalent regularization of Maxwell's equations

We study the scattering of time-harmonic electromagnetic waves by a closed or an open surfaces surrounded by an anisotropic medium. The corresponding system is non-elliptic and the "electric" and "magnetic" boundary conditions are non-normal. For the complex valued (non-real) frequency parameter the Dirichlet type "electric" boundary value problem (BVP) is equivalently reduced to the Neumann type "magnetic" BVP, which in final analysis is reduced to an equivalent elliptic BVP in a space of functions orthogonal to a certain vector. Using potential method and tools of pseudodifferential operators the unique solvability and regularity results of the equivalent BVPs are proved for real valued, constant, positive definite and symmetric permeability and permittivity matrices. The talk is based upon joint work with O. Chkadua and D. Kapanadze.