Sharp decay estimates for critical Dirac equations

William Borrelli (1) , Rupert L Frank (2, 3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CALTECH - California Institute of Technology
3 LMU - Ludwig Maximilian University [Munich] = Ludwig Maximilians Universität München

We prove sharp decay estimates for critical Dirac equations on R n , with n 2. They appear, e.g., in the study of critical Dirac equations on compact spin mani-folds, describing blow-up profiles (the so-called bubbles) in the associated variational problem. We establish regularity and integrability properties of L 2-solutions (where 2 is the Sobolev critical exponent of the embedding of H 1 2 (R n , C N) into Lebesgue spaces) and prove decay estimates, which are shown to be optimal proving the existence of a family of solutions having the prescribed asymptotic behavior.

Domaines: Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]; Analyse fonctionnelle [math.FA]

William Borrelli, Rupert L Frank. Sharp decay estimates for critical Dirac equations. 2018. ⟨hal-01865427v2⟩