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arXiv · 2606.16503

Nonexistence for screened Hartree energies

Dario Mazzoleni·Riccardo Moraschi·Berardo Ruffini
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Abstract

We develop an anti-concentration method for volume-constrained nonlocal shape optimization. Precisely, we apply it to prove the nonexistence of minimizers of an optimal design problem driven by a Hartree-type energy in the large mass regimes. The proof refines and extends the ideas from [Lu-Otto, CPAM 2014], where Lu and Otto dealt with nonexistence of minimizers for the Thomas-Fermi-Dirac-von Weizs\"acker energy. We also establish the asymptotic behavior of the associated isoperimetric profile of the energy.

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Dario Mazzoleni, Riccardo Moraschi, Berardo Ruffini. 2026-06-15. Nonexistence for screened Hartree energies. https://arxiv.org/abs/2606.16503

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