| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 86 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2023080 | |
| Published online | 08 December 2023 | |
On the shape of small liquid drops minimizing nonlocal energies
1
Dipartimento di Matematica, Università di Pavia, Via Adolfo Ferrata 5, 27100 Pavia, Italy
2
Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
3
Zentrum Mathematik, Technische Universität München, Boltzmannstrasse 3, 85748 Garching, Germany
* Corresponding author: fumihiko.onoue@tum.de
Received:
13
April
2023
Accepted:
8
November
2023
We study the equilibrium shape of liquid drops minimizing the fractional perimeter under the action of a potential energy. We prove, with a quantitative estimate, that the small volume minimizers are convex and uniformly close to a ball.
Mathematics Subject Classification: 49Q20 / 53A10 / 35R09 / 35R11
Key words: Fractional perimeter / isoperimetric problem / regularity of minimizers / liquid drop model
© The authors. Published by EDP Sciences, SMAI 2023
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