CCOR Optimization SeminarCsaba Farkas, professor at Sapientia Hungarian University of Transylvania, will hold a presentation entitled “Compact Sobolev embeddings on non-compact manifolds with applications” at the CCOR Optimization Seminar.
The abstract of the seminar:
Given a complete non-compact Riemannian manifold (M, g) with certain curvature restrictions, in this talk we introduce an expansion condition concerning a group of isometries G of (M, g) that characterizes the coerciveness of G in the sense of Skrzypczak and Tintarev (Arch Math 101(3): 259–268, 2013). Furthermore, under these conditions, compact Sobolev-type embeddings à la Berestycki-Lions are proved for the full range of admissible parameters (Sobolev, Moser-Trudinger and Morrey). We also consider the case of non-compact Randers-type Finsler manifolds with finite reversibility constant inheriting similar embedding properties as their Riemannian companions; sharpness of such constructions are shown by means of the Funk model. As an application, a quasilinear PDE on Randers spaces is studied by using the above compact embeddings and variational arguments.
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