Asymptotic of the dissipative eigenvalues of Maxwell’s equations

Abstract

Let Ω = R 3 ∖ K ¯, where K is an open bounded domain with smooth boundary Γ. Let V ( t ) = e t G b , t ⩾ 0, be the semigroup related to Maxwell’s equations in Ω with dissipative boundary condition ν ∧ ( ν ∧ E ) + γ ( x ) ( ν ∧ H ) = 0, γ ( x ) > 0, ∀ x ∈ Γ. We study the case when γ ( x ) ≠ 1, ∀ x ∈ Γ, and we establish a Weyl formula for the counting function of the eigenvalues of G b in a polynomial neighbourhood of the negative real axis.