9 mar 2005

Abstract.

Seminari di calcolo delle variazioni

when: Wednesday, March 9, at 4.30 pm NOT the usual time!!

where: Dipartimento di Matematica, sala delle riunioni

speaker: Olvier Druet (ENS, Lyon)

title: Compactness results for fourth order elliptic PDE's with exponential growth

abstract: On four-dimensional compact Riemmannian manifold, Paneitz discovered a fourth-order elliptic operator which has all the features of the Laplacian in dimension 2 (conformal invariance, curvature associated to this conformal invariance, relation with the Gauss-Bonnet-Chern-formula). We will investigate the blow-up behaviour of sequences of solutions of equations involving this type of operators. We shall see that multi-bubbling is forbidden which simplifies then a lot the analytical questions, compared to analoguous problems. I hope to give a rather complete proof of some compactness results for this type of equations.