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Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument
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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BibTeX
@misc{mazzoleni2026rigidity,
title = {{Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument}},
author = {Dario Mazzoleni and Riccardo Moraschi and Berardo Ruffini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29958},
eprint = {2610.29958},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29958},
}
RIS
TY - UNPB
TI - Rigidity of the ball for Hartree-type energies and second shape derivative via a continuity argument
AU - Dario Mazzoleni
AU - Riccardo Moraschi
AU - Berardo Ruffini
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29958
UR - https://arxiv.org/abs/2610.29958
AB - 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.
ER -