香蕉视频

Title: Blowing-up solutions for critical elliptic equations in low dimensions: the impact of the mass and the scalar curvature
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Abstract: In this talk, we will consider the question of existence of positive blowing-up solutions to a class of elliptic equations with critical Sobolev growth on a closed Riemannian manifold. A result of Olivier Druet provides necessary conditions for the existence of such solutions. We will present new results showing the optimality of Druet's conditions. We will see that the scalar curvature of the manifold plays a crucial role in this question. Furthermore, we will give special attention to the case of dimensions 4 and 5, where a mass term arises and plays an important role in the analysis. This is a joint work with Fr茅d茅ric Robert (Universit茅 de Lorraine).