On the Shape of Small Liquid Drops Minimizing Nonlocal Energies

2023/04/06 by Konstantinos Bessas, Bessas, Konstantinos, Matteo Novaga +3
Computer Science · Mathematics · #35R09 #35R11 #49Q20 #53A10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Dynamics and Fractals #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2304.03255

openalex publication_date 2023/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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