Blow-up examples for second order elliptic PDEs of critical Sobolev growth |
| |
Authors: | Olivier Druet Emmanuel Hebey |
| |
Institution: | Département de Mathématiques - UMPA, Ecole normale supérieure de Lyon, 46 allée d'Italie, 69364 Lyon cedex 07, France ; Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise cedex, France |
| |
Abstract: | Let be a smooth compact Riemannian manifold of dimension , and be the Laplace-Beltrami operator. Let also be the critical Sobolev exponent for the embedding of the Sobolev space into Lebesgue's spaces, and be a smooth function on . Elliptic equations of critical Sobolev growth such as have been the target of investigation for decades. A very nice -theory for the asymptotic behaviour of solutions of such equations has been available since the 1980's. The -theory was recently developed by Druet-Hebey-Robert. Such a theory provides sharp pointwise estimates for the asymptotic behaviour of solutions of . It was used as a key point by Druet to prove compactness results for equations such as . An important issue in the field of blow-up analysis, in particular with respect to previous work by Druet and Druet-Hebey-Robert, is to get explicit nontrivial examples of blowing-up sequences of solutions of . We present such examples in this article. |
| |
Keywords: | |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 |
|