Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument

Dario Mazzoleni; Riccardo Moraschi; Berardo Ruffini

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arXiv · 2610.29958

Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument

Dario Mazzoleni·Riccardo Moraschi·Berardo Ruffini

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Abstract

We study the second shape derivative of an optimal design functional involving a nonlocal term in order to prove rigidity of the ball. Our approach relies on a continuity argument that relates the second variation to that of the corresponding local problem. The model serves as a prototype for a broader class of shape optimization problems to which the same strategy may be adapted.

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Dario Mazzoleni, Riccardo Moraschi, Berardo Ruffini. 2026-10-21. Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument. https://arxiv.org/abs/2610.29958

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