Nonexistence of Minimizers for a Nonlocal Perimeter Functional with a Riesz and a Background Potential

2019/10/03 by Fumihiko Onoue, Onoue, Fumihiko
Computer Science · Mathematics · #28A75 #49J40 #49Q10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1910.01537

openalex publication_date 2019/10/03 · openalex created_date 2019/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel K, a Riesz potential, and a background potential in ℝ^N with N≥2 under the volume constraint. We show that the energy has no minimizer for a sufficiently large mass under suitable assumptions on K. The proof is based on the partition of a minimizer and the comparison of the sum of the energy for each part with the energy for the original configuration. This strategy is shown in [R.A. Frank, R. Killip, P.T. Nam, 2016] and [D.A. La Manna, 2018]

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