Asymptotic of the dissipative eigenvalues of Maxwell's equations

Abstract

Let $\Omega ={\mathbb{R}}^3\setminus \bar{K}$, where $K$ is an open bounded domain with smooth boundary $\Gamma$. Let $V(t)=e^{t{G}_b},t\ge 0,$ be the semigroup related to Maxwell's equations in $\Omega$ with dissipative boundary condition $\nu \wedge (\nu \wedge E)+\gamma (x)(\nu \wedge H)=0,\gamma (x)>0,\forall x\in \Gamma .$ We study the case when $\gamma (x)\ne 1,\forall x\in \Gamma ,$ 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.

Several misprints have been corrected