Electromagnetics in deterministic and stochastic bianisotropic media

Well-posedness
Theorem
Time-domain problems
Under suitable regularity assumptions on the data, (28) is weakly / mildly
/ strongly / classically well-posed.
The underlying space is H0(curl, O) × H(curl, O), where
H(curl, O) := {u ∈ (L 2 (O)) 3 : curl u ∈ (L 2 (O)) 3 }.
For bounded O, H0(curl, O) is the space
{u ∈ H(curl, O) : n × u|∂O = 0}.
The first component of the underlying space incorporates the perfect
conductor boundary condition for the electric field.
I. G. Stratis (Maths Dept, NKUA) Collège de France November 18, 2011 36 / 95