Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential

Onoue, Fumihiko

doi:10.4171/rsmup/93

Onoue, Fumihiko

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”

Résumé

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 $N \geq 2$ 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.

MR Zbl

DOI : 10.4171/rsmup/93

Classification : 49, 00

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     author = {Onoue, Fumihiko},
     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},
     volume = {147},
     year = {2022},
     doi = {10.4171/rsmup/93},
     mrnumber = {4450786},
     zbl = {1498.49085},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/93/}
}

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Onoue, Fumihiko. 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://www.numdam.org/articles/10.4171/rsmup/93/

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