2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60545The 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.12 pages, 3 figuresOptimization and ControlClassical Analysis and ODEs35R35; 49Q121text