Mixed boundary-value problems for Maxwell’s equations
Marius Mitrea · Transactions of the American Mathematical Society · 2009
We study the Maxwell system with mixed boundary conditions in a Lipschitz domain Ω \Omega in R 3 \mathbb {R}^3 . It is assumed that two disjoint, relatively open subsets Σ e \Sigma ^e , Σ h \Sigma ^h of ∂ Ω \partial \Omega such that Σ e ¯ ∩ Σ h ¯ = ∂ Σ e = ∂ Σ h \overline {\Sigma ^e}\cap \overline {\Sigma ^h}=\partial \Sigma ^e=\partial \Sigma ^h have been fixed, and one prescribes the tangential components of the electric and magnetic fields on Σ e \Sigma ^e and Σ h \Sigma ^h , respectively. Under suitable geometric assumptions on ∂ Ω \partial \Omega , Σ e