Isoperimetric problem with a Coulombic repulsive term

2012/07/03 by Vesa Julin, Julin, Vesa
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1207.0715

openalex publication_date 2012/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a non-local isoperimetric problem with a repulsive Coulombic term. In dimension three this corresponds to the Gamow's famous liquid drop model. We show that whenever the mass is small the ball is the unique minimizer of the problem. The proof is based on a strong version of a quantitative isoperimetric inequality.

Citations

• Regularity of the obstacle problem for a fractional power of the laplace operator

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