Diff. Geom, Math. Phys., PDE Seminar: Saikat Mazumdar

  • Date: 10/18/2016
  • Time: 15:30
Saikat Mazumdar, UBC

University of British Columbia


Higher order elliptic problems with critical sobolev growth on a compact riemannian manifold: Best constants and existence


We investigate the existence of solutions to a nonlinear elliptic problem involving 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 below 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 argument, we obtain a decomposition of Palais-Smale sequences as a sum of bubbles and adapt Lions's concentration-compactness lemma.

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Location: ESB 2012