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August  2008, 2(3): 335-340. doi: 10.3934/ipi.2008.2.335

## Resonances and balls in obstacle scattering with Neumann boundary conditions

 1 Department of Mathematics, University of Missouri, Columbia, Missouri 65211, United States

Received  January 2008 Revised  June 2008 Published  July 2008

We consider scattering by a smooth obstacle in $R^d$, $d\geq 3$ odd. We show that for the Neumann Laplacian if an obstacle has the same resonances as the ball of radius $\rho$ does, then the obstacle is a ball of radius $\rho$. We give related results for obstacles which are disjoint unions of several balls of the same radius.
Citation: T. J. Christiansen. Resonances and balls in obstacle scattering with Neumann boundary conditions. Inverse Problems & Imaging, 2008, 2 (3) : 335-340. doi: 10.3934/ipi.2008.2.335
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