Communications of the
Korean Mathematical Society CKMS

It is the purpose of this paper to study the reflection of solutions of Helmholtz equation with Neumann boundary data. In detail let $u$ be a solution of Helmholtz equation in the exterior of a ball in $\Real^3$ with exterior Neumann data $\rnd_{\nu} u=0$ on the boundary of the ball. We prove that $u$ can be extended to $\Real^3$ except the center of the ball. As a corollary, we prove that a sound hard ball can be identified by the scattering amplitude corresponding to a single incident direction and a single frequency.

Keywords: inverse problems

MSC numbers: Primary 65A99; Secondary 35X00