Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential
Rendiconti del Seminario Matematico della Università di Padova, Tome 147 (2022), pp. 111-137.
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corrigé par Erratum to “Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential”

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 volume 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.

DOI : 10.4171/rsmup/93
Classification : 49, 00 
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     author = {Fumihiko Onoue},
     title = {Nonexistence of minimizers for a nonlocal perimeter with a {Riesz} and a background potential},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {111--137},
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     year = {2022},
     doi = {10.4171/rsmup/93},
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     url = {http://archive.numdam.org/articles/10.4171/rsmup/93/}
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Fumihiko Onoue. Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential. Rendiconti del Seminario Matematico della Università di Padova, Tome 147 (2022), pp. 111-137. doi : 10.4171/rsmup/93. http://archive.numdam.org/articles/10.4171/rsmup/93/

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