On a perturbation of the poles of scattering matrix for varying baundary condition

S. V. Petras

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 12, Tome 117 (1981), pp. 183-191

Résumé

It is considered the behavior of the poles $z_n(\varepsilon)$, $n=1,2,\dots$ of scattering matrix of the operator $l_\varepsilon u=-\Delta u(x), x\in\Omega, \displaystyle\varepsilon\frac{\partial u}{\partial n}+\sigma(x)u|_{\partial\Omega}$ for $\varepsilon\to0$. It is proved that $|z_n(\varepsilon)-z_n|=O(\varepsilon^{\frac1{2q_n}})$ where $q_n$ is the order of pole $z_n$ of scattering matrix of the operator $l_0u=-\Delta u, u|_{\partial\Omega}=0$.