Voir la notice de l'article provenant de la source Numdam
Under suitable assumptions on , we show that, for ε>0 small and k large enough, problem (1) below has solutions which concentrate and blow-up as ε→0 at exactly k points; the blowing-up points approach as k→∞; the number of solutions tends to infinity as ε→0. These assumptions allow to be contractible and even arbitrarily close to starshaped domains.
On montre que, si satisfait certaines conditions, le problème (1) ci-dessous, pour ε>0 suffisamment petit et k grand, admet des solutions qui pour ε→0 se concentrent et explosent exactement en k points ; les points de concentration s'approchent du bord de quand k→∞ ; le nombre de solutions est arbitrairement grand pourvu que ε soit suffisamment petit. Parmi les ouverts bornés qui satisfont ces conditions il y en a aussi de contractibles, qui peuvent même être arbitrairement proches de ouverts étoilés.
Molle, Riccardo 1 ; Passaseo, Donato 2
@article{CRMATH_2002__335_12_1029_0,
author = {Molle, Riccardo and Passaseo, Donato},
title = {Nonlinear elliptic equations with critical {Sobolev} exponent in nearly starshaped domains},
journal = {Comptes Rendus. Math\'ematique},
pages = {1029--1032},
publisher = {Elsevier},
volume = {335},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02614-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/S1631-073X(02)02614-6/}
}
TY - JOUR AU - Molle, Riccardo AU - Passaseo, Donato TI - Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains JO - Comptes Rendus. Mathématique PY - 2002 SP - 1029 EP - 1032 VL - 335 IS - 12 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/S1631-073X(02)02614-6/ DO - 10.1016/S1631-073X(02)02614-6 LA - en ID - CRMATH_2002__335_12_1029_0 ER -
%0 Journal Article %A Molle, Riccardo %A Passaseo, Donato %T Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains %J Comptes Rendus. Mathématique %D 2002 %P 1029-1032 %V 335 %N 12 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/S1631-073X(02)02614-6/ %R 10.1016/S1631-073X(02)02614-6 %G en %F CRMATH_2002__335_12_1029_0
Molle, Riccardo; Passaseo, Donato. Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains. Comptes Rendus. Mathématique, Tome 335 (2002) no. 12, pp. 1029-1032. doi: 10.1016/S1631-073X(02)02614-6
Cité par Sources :