Energy asymptotics in the Brezis–Nirenberg problem: The higher-dimensional case - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematics in Engineering Année : 2020

Energy asymptotics in the Brezis–Nirenberg problem: The higher-dimensional case

Résumé

For dimensions N ě 4, we consider the Brézis-Nirenberg variational problem of finding Sp V q :" inf 0ıuPH 1 0 pΩq ş Ω |∇u| 2 dx` ş Ω V |u| 2 dx ş Ω |u| q dx¯2 {q , where q " 2N N´2 is the critical Sobolev exponent, Ω Ă R N is a bounded open set and V : Ω Ñ R is a continuous function. We compute the asymptotics of Sp0q´Sp V q to leading order as Ñ 0`. We give a precise description of the blow-up profile of (almost) minimizing sequences and, in particular, we characterize the concentration points as being extrema of a quotient involving the Robin function. This complements the results from our recent paper in the case N " 3.
Fichier principal
Vignette du fichier
bn-higherdim-fkk-revised.pdf (486.08 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03505329 , version 1 (30-12-2021)

Identifiants

Citer

Rupert L. Frank, Tobias König, Hynek Kovařík. Energy asymptotics in the Brezis–Nirenberg problem: The higher-dimensional case. Mathematics in Engineering, 2020, 2 (1), pp.119-140. ⟨10.3934/mine.2020007⟩. ⟨hal-03505329⟩
9 Consultations
35 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More