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A Priori Estimates for Finite-Energy Sign-Changing Blowing-Up Solutions of Critical Elliptic Equations

par Premoselli, Bruno
Référence International mathematics research notices, 2024, 6, page (5212-5273)
Publication Publié, 2024-03-01

Article révisé par les pairs

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Résumé :

We prove sharp pointwise blow-up estimates for finite-energy sign-changing solutions of critical equations of Schrödinger–Yamabe type on a closed Riemannian manifold (M, g) of dimension n ≥ 3. This is a generalisation of the so-called C0-theory for positive solutions of Schrödinger–Yamabe-type equations. To deal with the sign-changing case, we develop a method of proof that combines an a priori bubble-tree analysis with a finite-dimensional reduction, and reduces the proof to obtaining sharp a priori blow-up estimates for a linear problem.