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Towers of Bubbles for Yamabe-Type Equations and for the Brézis–Nirenberg Problem in Dimensions n≥ 7

par Premoselli, Bruno
Référence The Journal of geometric analysis, 32, 3, 73
Publication Publié, 2022-03-01

Article révisé par les pairs

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Résumé :

Let (M, g) be a closed locally conformally flat Riemannian manifold of dimension n≥ 7 and of positive Yamabe type. If h∈ C1(M) and ξ is a non-degenerate critical point of the mass function we prove the existence, for any k≥ 1 of a positive blowing-up solution uε of ▵guε+(cnSg+εh)uε=uε2∗-1that blows up, as ε→ 0 , like the superposition of k positive bubbles concentrating at different speeds at ξ. The method of proof combines a finite-dimensional reduction with the sharp pointwise analysis of solutions of a linear problem. As another application of this method of proof we construct sign-changing blowing-up solutions uε for the Brézis–Nirenberg problem ▵ξuε-εuε=