On characterization of balls via solutions to the Helmholtz equation
Abstract
A new analytical characterization of balls in the Euclidean space m is obtained. Unlike previous results of this kind, using either harmonic functions or solutions to the modified Helmholtz equation, the present one is based on solutions to the Helmholtz equation. This is achieved at the expense of a restriction imposed on the size of a domain -- a feature absent in the inverse mean value properties known before.
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