• Citer

Attaining the optimal constant for higher-order Sobolev inequalities on manifolds via asymptotic analysis

par Carletti, Lorenzo
Référence Journal of the London Mathematical Society, 111, 5, e70170
Publication Publié, 2025-05-01

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

Let (Formula presented.) be a closed Riemannian manifold of dimension (Formula presented.), and (Formula presented.) an integer such that (Formula presented.). We show that there exists (Formula presented.) such that for all (Formula presented.), (Formula presented.) where (Formula presented.) and (Formula presented.). Here, (Formula presented.) is the optimal constant for the Euclidean Sobolev inequality (Formula presented.) for all (Formula presented.). This result is proved as a consequence of the pointwise blow-up analysis for a sequence of positive solutions (Formula presented.) to polyharmonic critical nonlinear equations of the form (Formula presented.) in (Formula presented.). We obtain a pointwise description of (Formula presented.), with explicit dependence in (Formula presented.) as (Formula presented.).