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Some remarks on nonexistence in the Gamow liquid drop model
Abstract
In this paper we deal with the celebrated Gamow liquid drop model, namely, for m>0, N≥ 2 and α∈ (0,N), we study the problem min{P(Ω)+ Vα(Ω) : Ω⊂ ℝN, |Ω|=m} , and focus mostly on the nonexistence of minimizers for large masses. First we show that any possible minimizer in the asymptotic regime must satisfy an optimal thickness property. Eventually, in the simplified setting of sets made up as a tiling of cubes, we show that nonexistence occurs for large masses for the whole range of parameters N≥ 2 and α∈ (0,N).
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BibTeX
@misc{mazzoleni2026some,
title = {{Some remarks on nonexistence in the Gamow liquid drop model}},
author = {Dario Mazzoleni and Aldo Pratelli and Berardo Ruffini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16306},
eprint = {2610.16306},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16306},
}
RIS
TY - UNPB
TI - Some remarks on nonexistence in the Gamow liquid drop model
AU - Dario Mazzoleni
AU - Aldo Pratelli
AU - Berardo Ruffini
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16306
UR - https://arxiv.org/abs/2610.16306
AB - In this paper we deal with the celebrated Gamow liquid drop model, namely, for m>0, N≥ 2 and α∈ (0,N), we study the problem min{P(Ω)+ V_α(Ω) : Ω⊂ ℝ^N, |Ω|=m} , and focus mostly on the nonexistence of minimizers for large masses. First we show that any possible minimizer in the asymptotic regime must satisfy an optimal thickness property. Eventually, in the simplified setting of sets made up as a tiling of cubes, we show that nonexistence occurs for large masses for the whole range of parameters N≥ 2 and α∈ (0,N).
ER -