1208.5511 (Long Jin)

Resonance-free Region in scattering by a strictly convex obstacle    [PDF]

Long Jin

We prove the existence of a resonance free region in scattering by a strictly convex obstacle $\mathcal{O}$ with the Robin boundary condition $\partial_\nu u+\gamma u|_{\partial\mathcal{O}}=0$. More precisely, we show that the scattering resonances lie below a cubic curve $\Im\zeta=-S|\zeta|^{1/3}+C$. The constant $S$ is the same as in the case of the Neumann boundary condition $\gamma=0$. This generalizes earlier results on cubic poles free regions \cite{BLR}, \cite{HL} ,\cite{SZ5} obtained for the Dirichlet boundary condition.

View original: http://arxiv.org/abs/1208.5511