| Description: | [DMS-PDE Seminar] Dr Saikat Mazumdar (NTIS/ZCU, Czech Republic) -- Higher Order Elliptic Problems with Critical Sobolev Growth on a Compact Riemannian Manifold: Best Constants and Existence |
| Date: | Wednesday, Aug 24, 2016 |
| Time: | 11:30 a.m. - 12:30 p.m. |
| Venue: | 108, Lecture Hall Complex |
| Details: | We investigate the existence of solutions to a nonlinear elliptic problem involv- ing the critical Sobolev exponent for a Polyharmomic operator on a Riemannian manifold M. We first show that the best constant of the Sobolev embedding on a manifold can be chosen as close as one wants to the Euclidean one, and as a consequence derive the existence of minimizers when the energy functional goes be- low a quantified threshold. Next, higher energy solutions are obtained by Coron’s topological method, provided that the minimizing solution does not exist and the manifold satisfies a certain topological assumption. To perform the topological ar- gument, we obtain a decomposition of Palais-Smale sequences as a sum of bubbles and adapt Lions’s concentration-compactness lemma. |
| Calendar: | Seminar Calendar (entered by saugata.bandyopadhyay) |