• Citer

Einstein-Lichnerowicz type singular perturbations of critical nonlinear elliptic equations in dimension 3

par Premoselli, Bruno
Référence Discrete and continuous dynamical systems, 41, 11, page (5087-5103)
Publication Publié, 2021-11-01

Article révisé par les pairs

• Accès en ligne
• Détails
• Contenu
• Statistiques

Résumé :

On a closed 3-dimensional Riemannian manifold (M; g) we investigate the limit of the Einstein-Lichnerowicz equation 'Equation Presented' as the momentum parameter θ → 0. Under a positive mass assumption on Δg +h, we prove that sequences of positive solutions to this equation converge in C2(M), as θ → 0, either to zero or to a positive solution of the limiting equation Δgu + hu = fu5. We also prove that the minimizing solution of (1) constructed by the author in [15] converges uniformly to zero as θ → 0.