A note on some non-local variational problems

2021/07/25 by Davide Carazzato, Carazzato, Davide · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2107.11848

openalex publication_date 2021/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study two non-local variational problems that are characterized by the presence of a Riesz-like repulsive term that competes with an attractive term. The first functional is defined on the subsets of ℝ^N and has the fractional perimeter P_s as attractive term. The second functional instead is defined on L¹(ℝ^N;[0,1]) and contains an attractive term of positive-power-type. For both of the functionals we prove that balls are the unique minimizers in the appropriate volume constraint range, generalizing the results already present in the literature for more specific energies.

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• Continuity of critical points for 1-dimensional non-local energies

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