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.

Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

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

@article{RSMUP_2022__147__111_0,
     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://archive.numdam.org/articles/10.4171/rsmup/93/}
}

TY  - JOUR
AU  - Onoue, Fumihiko
TI  - Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2022
SP  - 111
EP  - 137
VL  - 147
UR  - http://archive.numdam.org/articles/10.4171/rsmup/93/
DO  - 10.4171/rsmup/93
LA  - en
ID  - RSMUP_2022__147__111_0
ER  -

%0 Journal Article
%A Onoue, Fumihiko
%T Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2022
%P 111-137
%V 147
%U http://archive.numdam.org/articles/10.4171/rsmup/93/
%R 10.4171/rsmup/93
%G en
%F RSMUP_2022__147__111_0

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://archive.numdam.org/articles/10.4171/rsmup/93/

Cité par Sources :