On shape optimization and the Pompeiu problem

Details On shape optimization and the Pompeiu problem On shape optimization and the Pompeiu problem

2000-12-11

arxiv.org/abs/math/0012077v1

Mathematics

Optimization and Control

12 pages, 3 figures

Scientific paper

The Pompeiu problem is considered as shape optimization problem. We show
stability of the ball which is the minimum point of related domain functional.
The proof is based on shape derivative method. Stability of the ball for
general domain functionals invariant under the rigid motions is discussed.

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