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. 111–137DOI 10.4171/RSMUP/93