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math.AP2026
Some remarks on nonexistence in the Gamow liquid drop model
Dario Mazzoleni, Aldo Pratelli, Berardo Ruffini
In this paper we deal with the celebrated Gamow liquid drop model, namely, for , and , we study the problem \[ \min\Big\{P(Ω)+ V_α(Ω) : Ω\subset \mathbb{…
math.AP2026
Nonexistence for screened Hartree energies
Dario Mazzoleni, Riccardo Moraschi, Berardo Ruffini
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 prob…
math.AP2026
Existence and Regularity in the Small-Mass Regime for a Hartree--Ohta-Kawasaki Shape Optimization Problem
Dario Mazzoleni, Riccardo Moraschi, Berardo Ruffini
We consider a shape optimization problem for a hybrid energy combining local confinement and nonlocal Coulomb repulsion. Specifically, for any open set of…