Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential
Fumihiko Onoue
Scuola Normale Superiore di Pisa, Italy
![Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-rsmup-volume-147.png&w=3840&q=90)
Abstract
We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel , a Riesz potential, and a background potential in with under the volume constraint. We show that the energy has no minimizer for a sufficiently large volume under suitable assumptions on . 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.
Cite this article
Fumihiko Onoue, Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential. Rend. Sem. Mat. Univ. Padova 147 (2022), pp. 111–137
DOI 10.4171/RSMUP/93