JournalsrsmupVol. 147pp. 111–137

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
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Abstract

We consider the nonexistence of minimizers for the energy containing a nonlocal perimeter with a general kernel KK, a Riesz potential, and a background potential in RN\mathbb{R}^N with N2N\geq2 under the volume constraint. We show that the energy has no minimizer for a sufficiently large volume under suitable assumptions on KK. 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