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

created by onoue on 07 Oct 2019
modified on 28 Nov 2019

[BibTeX]

Preprint

Inserted: 7 oct 2019
Last Updated: 28 nov 2019

Year: 2019

ArXiv: 1910.01537 PDF

Abstract:

We consider the nonexistence of minimizers for a energy containing a nonlocal perimeter with a general kernel $K$, a Riesz potential, and a background potential in $\mathbb{R}^N$ with $N\geq 2$ under the volume constraint. We show that the energy has no minimizer with 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.L. Frank, R. Killip, and P.T. Nam, (2016)] and [D.A. La Manna, (2018)].