Electron. J. Diff. Eqns., Vol. 2006(2006), No. 154, pp. 1-5.

A characterization of balls using the domain derivative

Andriy Didenko, Behrouz Emamizadeh

Abstract:
In this note we give a characterization of balls in $\mathbb{R}^N$ using the domain derivative. As a byproduct we will show that an overdetermined Stekloff eigenvalue problem is solvable if and only if the domain of interest is a ball.

Submitted September 28, 2006. Published December 14, 2006.
Math Subject Classifications: 35J25, 35P99.
Key Words: Domain derivative; overdetermined problems; Stekloff problem.

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Andriy Didenko
Department of Mathematics
The Petroleum Institute
P.O. Box 2533
Abu Dhabi, UAE
email: adidenko@pi.ac.ae
Behrouz Emamizadeh
Department of Mathematics
The Petroleum Institute
P.O. Box 2533
Abu Dhabi, UAE
email: bemamizadeh@pi.ac.ae

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