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.
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”

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 
@article{RSMUP_2022__147__111_0,
     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},
     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/}
}
TY  - JOUR
AU  - Fumihiko Onoue
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://www.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 Fumihiko Onoue
%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://www.numdam.org/articles/10.4171/rsmup/93/
%R 10.4171/rsmup/93
%G en
%F RSMUP_2022__147__111_0
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://www.numdam.org/articles/10.4171/rsmup/93/

Cité par Sources :